The man, Eric Goodridge, died from homicidal violence, including gagging and neck compression, said Ellen Borakove, a spokeswoman for the city medical examiner's office.
Sources tell WCBS-TV the victim was castrated.
Police had not released an identification of the woman. Officer Martin Speechley said her identity was known to authorities, and "we're still looking for her."
The New York Post reports the suspect was the man's daughter who was taken to a mental ward Sunday.
The New York Daily News says the suspect was his stepdaughter, seeking to exact revenge for alleged sexual abuse two decades ago. That paper says she checked herself into a mental hospital.
Both papers identify her as Brigitte Harris, 26, who lived in the apartment in which Goodridge was found. Both also say the man was already dead when he was mutilated.
A police report said the victim, who was from Staten Island, was found unconscious in an apartment early Saturday afternoon and died at the scene, but it offered few other details.
According to the Daily News, police said Harris lured Goodridge to her apartment with e-mail messages. She left notes in her apartment accusing Goodridge of sexual abuse.
"This is a homicide that had meaning and reason," one source told the paper.
Newspaper reports, quoting police and witnesses, said the man was found in the top-floor apartment of the three-story house, where the woman was the tenant. Reports said she worked in airport security, but a Transportation Security Administration spokesman denied she was an employee. However, the Daily News said Harris works for a private security company at Kennedy Airport.
Goodridge was a native of Liberia. WCBS-TV's Lou Young got the impression his neighbors on Staten Island did not feel any sympathy for him.