Within the gloomy cement hallways of a public housing complex at Fort Greene, Walt Whitman Residence, where chicken bones, abandoned mattresses, and other trash litter the grass, the murder of 66-year-old Corine Perkins over the New Year’s weekend has raised more questions than answers.

How, many wondered, could the feisty Ms. Corine, as she was known, be strangled to death while her granddaughter, sleeping in the same apartment, didn’t notice a struggle? More importantly: What kind of person could murder the Brooklyn neighborhood’s cherished matriarch?

“Only a senseless animal,” Council Member Letitia James, who represents the area, said yesterday, announcing a $500 reward for information leading to the arrest of the killer. The co-founder of the group 100 Blacks of Law Enforcement Who Care, Lieutenant Eric Adams, also pledged $1,000.

“The streets talk,” Lieutenant Adams, of the nearby 88th Precinct, said, expressing confidence an arrest would be made.

According to police reports, the woman’s body was found around 9:45 a.m. on New Year’s Day by one of her grandchildren. When he opened the apartment door, he told police, it was unlocked. After entering he found Perkins on the floor in her bedroom, slumped against the bed in her brown nightgown. There was a telephone cord wrapped around her neck. Death by strangulation, according to a preliminary autopsy conducted by the medical examiner, was the cause of death.

There were no signs of forced entry, police said.

“It is a complete mystery, lost on me, lost on everyone,” Justine Bastien, one of Perkins’s six children, said yesterday, dabbing at tears around her eyes as she stood outside Walt Whitman. Ms. Bastien said she and her mother had a telephone conversation around 9:45 on New Year’s Eve, chatting, as they did every day, about “small things, nothing stuff, just this and that.” Perkins did not have any plans for New Year’s, Ms. Bastien said, and had settled in for a quiet night in her three-bedroom apartment.

No suspects have yet been named, police said.

“We will find him, we will find him,” the executive director of the Fort Greene Youth Foot Patrol, Edwin Carter, said. He was a friend of Perkins’s for more than 40 years.

Mr. Carter, who is blind and calls himself the neighborhood’s patriarch, also said local teenagers were so angered over the murder that, should they find the culprit, “they would rope him up over a telephone pole like a pair of old shoes.”

Mr. Carter said he first met Perkins when she left her family in Colquitt, a rural town in Georgia, and migrated with her husband and first child, both now deceased, to Brooklyn. It was in 1965 that she moved into apartment 2E at Walt Whitman, where she was killed.

She was known, among other things, to decorate the cold walls of the complex at Christmastime, to dish out biscuits and barbecued chicken in the summers, and to make the old-time kind of caramel cake when most had forgotten how.

“She was special,” Mr. Carter said, “as a mother, a great-grandmother, and a great-great-grandmother, to everyone.”

She also helped to change Fort Greene from dangerous to chic. Eleven years ago there were 25 murders reported in the precinct and 1,118 robberies, according to police statistics. Those numbers have been reduced dramatically. Last year, four murders were recorded and 310 robberies.