The police and the city medical examiner's office yesterday were investigating the death of a 5-year-old Bronx girl who was found on Sunday dangling from a closet door with a jump-rope around her neck.

The authorities disclosed little about the death yesterday, but a police official who spoke on the condition of anonymity because the cause of death had not been determined said that detectives thought the girl had accidentally become tangled in the rope as she tried to swing from the closet door to her bed.

Early news reports said that the girl, whom the police identified yesterday as Monet Fulgham, had been raped, but the police later denied that assertion.

The police said they responded to a call from the girl's grandmother in the seventh-floor apartment in the Boston Secor Houses at 3475 Bivona Street in Eastchester at 5:40 p.m. on Sunday. The grandmother had come upon Monet hanging from the rope and lowered her to the floor before calling 911 for help.

Monet was taken to Our Lady of Mercy Hospital, where she was pronounced dead on arrival. Grace Brugess, a spokeswoman for the medical examiner, said late yesterday that the cause of death had not been determined.

The source of the reports that Monet had been raped, attributed to unnamed police officials, was unclear yesterday. But neighbors and acquaintances of the girl and her family, some of whom wept and embraced one another when they stopped by the Eastchester apartment yesterday, said they were angered by the mere suggestion of such a heinous crime.

''I can't believe the R word was affiliated with her name,'' said Paulette Young, 24, a dance teacher who lives in the housing project.

Tamaira Capehart, 27, who lives on the eighth floor of the building and is a criminal justice student at John Jay College, said Monet's death could only have been an accident.

''I don't think, I know,'' Ms. Capehart said. ''Monet was an active child that you had to keep an eye on.''

Quaheem Carter, a maintenance worker who lives in the complex, said that Monet lived with her grandmother, Miriam Williams; her mother, Jackie Williams; an aunt, Joyce Williams; and Joyce's three children, ranging in age from 13 to 1.

He said a cousin of Monet's who is known as Bud and is in his early 20s also lived in the apartment, but other neighbors said that he might have been simply a frequent visitor, and that they did not know if he was in the apartment when Monet became tangled in the rope.

Sheila Stainback, a spokeswoman for the city's Administration for Children's Services, said the case was under investigation. She declined to say if the agency had any record of complaints about negligence or abuse in Monet's family.

The same police official who shared the theory of the accident said that officers who responded to the grandmother's call found Monet lying on a couch and that it was unclear if the girl was alive at that time.

The police official said the girl's jump-rope had either been tied or become caught in a doorjamb, and could have been fashioned into something a small child would use to swing a few feet to a bed.

Edna Ford, 70, another neighbor and a retired nurse's aide, said that Monet was ''always moving, climbing, jumping on the bed.''

''All she ever did was dance, shake her little butt with her Pampers on,'' said Ms. Ford. She said Monet had always called her Grandma.

''I'll probably see her in my sleep,'' Ms. Ford said. ''She'll probably tell me, 'Bye, Grandma.' ''