Troopers say 49-year-old Abbas Lodhi and his sons, 9-year-old Zain Lodhi and 13-year-old Mugthba Lodhi, were found dead from gunshot wounds Thursday.
They say another family member, 43-year-old Sarwat Lodhi, is still missing. Police did not specify her relationship to the other three.
Police called the deaths a "family tragedy" and said there is no public danger.
Troopers said Abbas Lodhi and one of the boys were found dead inside a car parked at a supermarket in the Dutchess County town of Pleasant Valley, 75 miles north of New York City. The second boy was found dead at a residence.