Suffolk County police found the body of 33-year-old Elizabeth Hernandez, a mother of two, in her Shirley house around 12:30 p.m. Wednesday. The boyfriend also lived there, officials said.
Detective Lieutenant Jack Fitzpatrick said investigators "would like to speak with the boyfriend. He is conspicuous in his absence."
He said police have been called to the home on numerous occasions.
A neighbor tells NBC 4 New York the couple had previous domestic problems.
The medical examiner will determine the cause of death.
Anyone with information is asked to call Crime Stoppers at 1-800-220-TIPS.