The victim, about 55 years old, was found dead in another apartment on the floor where she lived on East 187th Street in the Belmont section.
Her identity has not yet been released. Investigators say she had been stabbed several times.
"I feel bad because she was a real good person. I mean she didn't bother anybody. I mean I rarely saw but when I did, she was OK," said a neighbor, Roseann Delvalle, who added that the woman lived alone.
Police found the victim's body in a pool of blood at about 5:45 Wednesday morning.
Investigators say her pants and underwear were down, suggesting a sexual assault before the fatal attack.
Furthermore, the victim was found several doors down the hall on the third floor.
"The residents of the apartment moved out about a week ago and the woman's body was found in the vacant apartment and we are in the process of identifying that woman," said Police Commissioner Ray Kelly.
Crime scene investigators searched a second story roof that could have provided an escape route for the attacker.
Police recovered one knife but indicated it was not the one used in the assault.
Neighbors told us the 17-story apartment building is a haven for drug activity and that several drug rehab programs are based here.
"I really want to move. I don't even want my kids coming outside. This neighborhood is horrible. There's too many shootings. There's just a lot going on," said buiilding resident Maleeva Elliott.