The men, who both lived in the facility on West 132nd Street, got into a fight on the fifth floor sometime before 9 a.m. Friday.
A 44-year-old man was stabbed multiple times and pronounced dead.
A 39-year-old man was stabbed once to the neck and is in critical condition at Harlem Hospital.
Detectives said the two stabbed each other during an ongoing dispute.
A knife was recovered and police are interviewing witnesses to determine what happened.