WESTMINSTER, Colo. -- Police said Tuesday the abduction and killing of a 10-year-old girl in suburban Denver this month is connected to a May kidnapping attempt in which a woman fought off a stranger who grabbed her from behind and put a rag over her mouth that smelled of chemicals.

The 22-year-old woman was jogging when a man attacked her May 28, Memorial Day, authorities said. It happened at a lake near the Westminster elementary school where Jessica Ridgeway was headed when she disappeared Oct. 5.

Jessica's body was found Oct. 10 in a nearby field.

Police didn't say why they believe the two cases are related. But Westminster investigator Trevor Materasso said Tuesday authorities are looking for a suspect in both attacks who they describe as a "light-skinned man" between 18 and his mid-30s of average height and build.

"That's starting to create a black-and-white silhouette that, with evidence, we'll eventually be able to put a face to," Materasso said.

The jogger attack happened at Ketner Lake. Several trails leading to the lake and a surrounding open-space park are across the street from Witt Elementary School, where Jessica was headed when she was abducted.

Police said the man who attacked the jogger put a rag that smelled of chemicals over her mouth, but she managed to fight him off. Materasso said investigators haven't been able to determine if the substance on the rag was meant to subdue the woman.

"It could have been a rag from a garage or something," Materasso said.

Based on the proximity of the two cases, investigators believe the suspect is familiar with the area, either because he lived in the neighborhood in the past, has friends or family there, or has frequented the area for business or recreation.

More than 1,000 officers and 10 agencies, including the FBI, have investigated the case, following up on more than 4,000 leads.

With Jessica's killer still at large, high school students have volunteered to walk younger students to class to keep them safe and more parents are waiting at bus stops with their children and dropping them off at school.

The number of suspected abduction attempts reported to police also has increased, possibly because more children and parents are on alert for suspicious behavior.

Police have not ruled out two child enticement cases reported in Arvada in September or an attempted abduction of a woman Oct. 16 in Aurora.

Authorities also are methodically looking at sex offenders in the neighborhood, both registered and unregistered; reports of lewd or suspicious behavior; and cases involving crimes that have not yet been prosecuted.

"We don't want the community to focus on sex offenders who have cooperated with the law," Materasso said. "We're asking the community to focus on odd behavior."

Information about clues found so far and released to the public include the discovery of Jessica's backpack in Superior, about 7 miles northwest of her house, and a 1-inch by 1 1/2-inch cross that Materasso said is a "pivotal piece" of information.

"We're more focused on both an individual and a cross," Materasso said.

In response to requests from the public, police are working with Metro Denver Crime Stoppers to establish a reward fund for information leading to the arrest of Jessica's killer.

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  • Austin Reed Sigg

    This booking photo released by the Westminster, Colo., Police Department shows Austin Reed Sigg. Police in this Denver suburb announced Wednesday, Oct. 24, 2012, that Sigg, 17, has been arrested in the abduction and killing of a 10-year-old girl and the attempted kidnapping of a runner. Police say they arrested Sigg at his Westminster home Tuesday night, about five miles from the home of Jessica Ridgeway, who disappeared Oct. 5. Her body was found five days later in a field at a park. The break comes two days after police said Jessica's abduction was linked to the attempted abduction in May of a 22-year-old runner at another park. (AP Photo/Westminster Police Department)

  • Missing School Girl

    This image provided by the Westminster Colorado Police Department shows 10-year-old Jessica Ridgeway. Police in Westminster are looking for a 10-year-old girl who was last seen walking to school. Jessica Ridgeway normally meets a friend at a park on her way to Witt Elementary School, but she didn’t make it to the park or school Friday Oct. 5, 2012. An Amber Alert has been issued. (AP Photo/Westminster Colorado Police Department)

  • Scott Storey

    District Attorney Scott Storey talks to the media after a hearing for Austin Reed Sigg, 17, the suspect in connection with the death of 10-year-old Jessica Ridgeway at the Jefferson County Courthouse in Golden, Colo., on Thursday, Oct. 25, 2012. Ridgeway disappeared Oct. 5 after leaving home for school. Her remains were found 5 days later. (AP Photo/Ed Andrieski)

  • Sigg Home

    Investigators are pictured at the home of Austin Reed Sigg, 17, where they spent a second day gathering evidence in Westminster, Colo., on Thursday, Oct. 25, 2012. Sigg is the suspect arrested in connection with the death of 10-year-old Jessica Ridgeway who disappeared Oct. 5 after leaving home for school. Her remains were found 5 days later. (AP Photo/Ed Andrieski)

  • Sigg Home

    A Westminster Police Officer is surrounded by police vehicles at the home of Austin Reed Sigg, 17, where investigators spent the second day gathering evidence in Westminster, Colo., on Thursday, Oct. 25, 2012. Sigg is the suspect arrested in connection with the death of 10-year-old Jessica Ridgeway who disappeared Oct. 5 after leaving home for school. Her remains were found 5 days later. (AP Photo/Ed Andrieski)

  • Scott Story, Pete Weir

    District Attorney Scott Story, right, and assistant Pete Weir leave district court after a hearing in the case against Austin Reed Sigg, 17, in Golden, Colo. on Tuesday, Oct. 30, 2012. Sigg is the suspect arrested in connection with the death of 10-year-old Jessica Ridgeway who disappeared Oct. 5 after leaving home for school. Her remains were found 5 days later. It was announced in court that Sigg would be tried as an adult in connection with her death. (AP Photo/Ed Andrieski)

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Wooden cross photo from <a href="http://www.facebook.com/westminsterpolice?fref=ts">Westminster PD</a>.

  • Wooden cross photo from <a href="http://www.facebook.com/westminsterpolice?fref=ts">Westminster PD</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • 150105_10151341575584305_1291829664_n

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    Via <a href="http://www.facebook.com/media/set/?set=a.10151340500824305.521112.141296864304&type=1">Westminster PD's Facebook page</a>.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Department released new photos of missing 10-year-old Jessica Ridgeway. The picture is dated June 25th, 2011.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is dated July 6, 2006.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo of Jessica is dated July 13, 2006.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Jessica Ridgeway

    The Westminster Police Dept. provided <a href="http://www.facebook.com/pages/Westminster-PD/141296864304">new photos of missing 10-year-old Jessica Ridgeway on their Facebook page</a> Tuesday. Jessica has been missing since Friday Oct. 5th. This photo is undated.

  • Arvada Police spokeswoman Jill McGranahan, left, and Westminster Police spokesman Trevor Materasso, right, address the media regarding a body found lat Wednesday in Parttridge Park in Arvada during a press conference at the Westminister Police Department Thursday, Oct. 11, 2012 in Westminister, Colo. The search missing 10-year-old Jessica Ridgeway will continue, police said Thursday. (AP Photo/Barry Gutierrez)

  • Missing School Girl

    A police officer walks through a field of tall grass searching for ten-year-old Jessica Ridgeway near her home in Westminster, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Missing School Girl

    Denis McLaughlin leads his search and rescue dog through a field of tall grass searching for ten-year-old Jessica Ridgeway near her home in Westminster, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Missing School Girl

    Members of a search and rescue team use a dog while searching for ten-year-old Jessica Ridgeway near her home in Westminster, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Missing School Girl

    A member of a search and rescue team leads his dog through a field of tall grass searching for ten-year-old Jessica Ridgeway near her home in Westminster, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Missing School Girl

    A Westminster police officer sits in her partrol car at the home of ten-year-old Jessica Ridgeway in Westminster, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Missing School Girl

    A missing poster for ten-year-old Jessica Ridgeway is seen in Broomfield, Colo., on Monday, Oct. 8, 2012. The youngster has been missing since she left her home Friday morning on her way to school. (AP Photo/Ed Andrieski)

  • Arvada Police spokeswoman Jill McGranahan, left, and Westminster Police spokesman Trevor Materasso, right, address the media regarding a body found lat Wednesday in Parttridge Park in Arvada during a press conference at the Westminister Police Department Thursday, Oct. 11, 2012 in Westminister, Colo. The search missing 10-year-old Jessica Ridgeway will continue, police said Thursday. (AP Photo/Barry Gutierrez)

  • Police search near an area where a body was found Wednesday in Parttridge Park, in Arvada, Colo., during the ongoing search for missing 10-year-old Jessica Ridgeway on Thursday, Oct. 11, 2012. Police are not saying whether the body found is linked to the missing girl case and noted Thursday that officers are still searching for Ridgeway, who disappeared Oct. 5. (AP Photo/Barry Gutierrez)

  • Police search near an area where a body was found Wednesday in Parttridge Park, in Arvada, Colo., during the ongoing search for missing 10-year-old Jessica Ridgeway on Thursday, Oct. 11, 2012. Police are not saying whether the body found is linked to the missing girl case and noted Thursday that officers are still searching for Ridgeway, who disappeared Oct. 5. (AP Photo/Barry Gutierrez)

  • Police search near an area where a body was found Wednesday in Parttridge Park, in Arvada, Colo., during the ongoing search for missing 10-year-old Jessica Ridgeway on Thursday, Oct. 11, 2012. Police are not saying whether the body found is linked to the missing girl case and noted Thursday that officers are still searching for Ridgeway, who disappeared Oct. 5. (AP Photo/Barry Gutierrez)

  • Police search near an area where a body was found Wednesday in Parttridge Park, in Arvada, Colo., during the ongoing search for missing 10-year-old Jessica Ridgeway on Thursday, Oct. 11, 2012. Police are not saying whether the body found is linked to the missing girl case and noted Thursday that officers are still searching for Ridgeway, who disappeared Oct. 5. (AP Photo/Barry Gutierrez)

  • Police search near the 9800 block of Alkire St. on the west side of Stanley Lake in Arvada, Colo., during the ongoing search for missing 10-year-old Jessica Ridgeway on Thursday, Oct. 11, 2012. Police are not saying whether a body found in Pattridge Park on Wednesday is linked to the missing girl case and noted Thursday that officers are still searching for Ridgeway, who disappeared Oct. 5. (AP Photo/Barry Gutierrez)