NEW YORK — A mother returned home to her luxury apartment building near Central Park on Thursday to find two of her small children stabbed to death in a bathtub and their nanny, with self-inflicted stab wounds, lying near them, police said.

The nanny, who was found near a knife, was hospitalized in critical condition and was in police custody, and authorities said she is suspected of killing the children, who were pronounced dead at a hospital.

The children's father, CNBC digital media executive Kevin Krim, who had been away on a business trip, was met by police at the airport on his return and was given an escort to the hospital where his loved ones had gathered.

The couple's apartment building sits in one of the city's most idyllic neighborhoods, a block from Central Park, near the Museum of Natural History and blocks from Lincoln Center for the Performing Arts. The neighborhood is home to many affluent families, and seeing children accompanied by nannies is an everyday part of life there, making the idea of such violence even more disturbing to residents.

Music therapist Rima Starr, who lives on the same floor as the Krim family, said she heard screams coming from the family's apartment at around 5:30 p.m.

"There was some kind of screaming about, `You slit her throat!'" she said. "It was horrible."

The children's mother, Marina Krim, had entered the dark apartment with her 3-year-old and initially thought her other two children were out with the 50-year-old nanny, police Commissioner Raymond Kelly said. She went downstairs and asked the doorman at her building, La Rochelle, on Manhattan's Upper West Side, whether he'd seen them leave. When he said no, she went back upstairs and discovered her 1-year-old son, Leo, and her 6-year-old daughter, Lucia, known as LuLu, in the bathroom, Kelly said. It's unclear how many times the children were stabbed.

The nanny was found on the bathroom floor with stab wounds to her neck, and a kitchen knife was close by, police said. There was no water in the bathtub, they said.

Kelly said it's unclear how long the nanny had worked for the family and the police investigation was ongoing. No charges had been filed.

Starr, the family's neighbor, said she believed the nanny had been hired just recently.

"I met her in the elevator, the day before yesterday, and was making small talk," she said.

After police arrived, she said, the mother remained in the building's lobby, screaming hysterically and clutching her surviving child.

On a webpage devoted to a recent family wedding, the eldest of the children, LuLu, is described as loving "art projects, ballet, and all things princess." The youngest, Leo, was said to be just learning how to walk.

The family had moved to New York from San Francisco within the last few years. The children's father was named general manager of CNBC's digital media division in March, after working previously in digital media at Bloomberg. Their mother had a cooking blog and taught art classes to young children.

The family lived in a stately, late 19th-century apartment building where one three-bedroom unit currently available for rent has an asking price of $10,000 per month. They had a greyhound, retired from racing, named Babar.

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Associated Press writer David B. Caruso contributed to this report.