NEW YORK (AP) _ The still-unconscious victim of a vicious daylight beating near a Central Park playground was identified today as a talented pianist who dreamed of playing at Carnegie Hall.

However, the 32-year-old woman's name was not released because she may have been sexually assaulted in the attack three days ago.

Two of the victim's sisters and their husbands were at her hospital bedside, Mayor Rudolph Giuliani said today. Her parents were vacationing and had not been located, he said.

Saying ``We're praying for her,'' Giuliani described her condition at New York Hospital-Cornell Medical Center as still ``critical, life-threatening.''

No arrests had been made.

The woman was found Tuesday afternoon by Iris Fass as she walked a dog in a well-trafficked section of the park, near a playground and yards from a busy avenue and the fashionable Upper West Side.

``I was screaming, `a woman is bleeding to death!' But the people in the playground looked up and then went back to doing what they were doing,'' Fass said.

The attack was described as an apparent attempted rape.

Police found no identification. Three people, described as neighbors and colleagues from work, called police to identify her from a police sketch, saying she was a resident of a West 57th Street apartment.

Comparing the victim's fingerprints with prints found in the apartment confirmed her identity, Police Commissioner Howard Safir said.

The woman delighted neighbors when she played piano at home, said Dan Ranger, who said he lives next door to her. He compared her to Marian, the librarian in ``The Music Man,'' and said she was ``a nice, sweet girl.''

Other neighbors said the woman, who moved here from New Jersey, gave music lessons, used to play in the showroom of piano maker Steinway & Sons and dreamed of performing in nearby Carnegie Hall.

``The one thing I know about her, is that she would never provoke anything,'' Ranger said.

The attack brought back memories of two other vicious attacks on women in the park New Yorkers often see as a peaceful refuge.

Last September, a jogger was killed in the park's northern end. Her attacker was never found. That slaying happened not far from where another runner was raped and beaten by a teen-age gang in 1989. Both of those women were attacked in a more remote area of the park and in off-hours, one at night and the other in the early dawn.