The victims of the 10:15 p.m. EDT Friday blaze were identified as Jennifer McCusker, 41, of Shirley, Aidan Tarbell, 7, and twin brother and sister Brendan and Ava Jane Mistretta, The New York Times reported.
Christopher Mehrman, the chief fire marshal for the town of Brookhaven, told the newspaper it appeared the fire was accidental.
Suffolk County police Detective Lt. Jack Fitzpatrick said it appeared the fire started in the home's living room.
McCusker was found in a bedroom in the rear of the house where the twins slept. Fitzpatrick said it appeared as if McCusker were trying to rescue the children before she was overcome by smoke.
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