LONDON -- A 7-year-old girl who survived the grisly shooting in the French Alps that killed her parents and grandmother left a French hospital Friday to return to Britain, though police could not say how soon she might be questioned about the murders.

Zaina al-Hilli, who was shot in the shoulder and severely beaten, emerged on Sunday from a medically-induced coma and was traveling from France back to Britain, where the family lived, Surrey Police said.

Police would not confirm who was accompanying Zaina back to the U.K., or comment on the role the child might play in assisting French and British detectives investigating the case. Britain's Foreign Office, which had been offering support to the girl, declined to comment.

British-Iraqi engineer Saad al-Hilli, his wife Iqbal, her mother and an unrelated French cyclist were shot dead last week in a quiet wooded area near France's Lake Annecy. Zaina was found covered in blood and suffering from head injuries by a passerby. Her 4-year-old sister Zeena was left unharmed, but lay undiscovered for eight hours – huddled under the legs of her deceased mother.

The young British sisters are the only known witnesses to the crime, and the elder daughter is now regarded as crucial to the investigation.

William Brett Martin, the cyclist who was first to arrive at the scene of the killings, said he found Zaina stumbling along the ground outside the car in which her family had been shot dead. He told BBC television in an interview Thursday that the girl was covered in blood and had "obvious head injuries."

French prosecutor Eric Maillaud has said he believes the key to solving the execution-style killings is in the U.K., where French police are now carrying out inquiries – suggesting that there may be a connection to the al-Hilli family's personal or professional life in the southern English county of Surrey, where they settled after leaving Iraq.

A family dispute, al-Hilli's job as a satellite communications engineer, or the family's Middle Eastern origins have all be suggested as potential motives for the slayings.

Family friends have described a dispute between Saad al-Hilli and his brother Zaid over their father's inheritance, although French authorities have said Zaid denies that there was a disagreement.

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  • Crime coordinator Capt. Laurent Dourel, left, Annecy prosecutor Eric Maillaud, second left, and French Gendarmes Col. Bertrand Francois, third left, and Lt. Col. Benoit Vinneman atttend a news conference in Annecy, French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Lionel Cironneau)

  • Annecy prosecutor Eric Maillaud answers a question during a news conference in Annecy, France, on Thursday, Sept. 6, 2012. (AP Photo/Lionel Cironneau)

  • A gendarme blocks access to the site where people were shot to death near Chevaline, French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Laurent Cipriani)

  • A Gendarme's car heads to a killing site near Chevaline, the French Alps, on Wednesday, Sept.5, 2012. (AP Photo/Alexis Moro)

  • Gendarmerie Col. François, left, and Annecy prosecutor Eric Maillaud answer reporter near a killing site, near Chevaline, the French Alps, on Wednesday, Sept. 5, 2012. (AP Photo/Alexis Moro)

  • Gendarmes block access to a killing site near Chevaline, the French Alps, on Wednesday, Sept. 5, 2012. (AP Photo/Alexis Moro)

  • Gendarmes blocks access to site where people were shot to death near Chevaline, the French Alps, on Thursday, Sept. 6, 2012. (AP Photo/Laurent Cipriani)