Police Commissioner Ray Kelly identified the killer as the victim's 38-year-old "emotionally disturbed adopted sister," with whom she lives.
The woman fled the scene, but was arrested after assaulting another woman.
She was taken to Queens Hospital Center for psychiatric evaluation. Charges are pending.
Hill was stabbed multiple times, with pieces of her head cut off.
She may have had a loud argument with the adopted sister before she was killed.
Kelly said investigators are looking into claims by neighbors that they called 911, but police did not respond.