Arson detectives are investigating a fire at an Academy Award-nominated composer’s house in Amagansett at the start of the July Fourth weekend. The house was occupied at the time.East Hampton Town detectives and the Suffolk Police Department’s arson squad are in the early stages of the investigation, according to Det. Sgt. Greg Schaeffer, who was briefed on the case. “We’re treating it as a suspicious fire at this time,” he said.The detective declined to say whether arson had been positively identified as the cause until town police receive a complete report from the county squad, which collected evidence in the hours after the fire. Among the criteria being studied is whether accelerant was used.The Amagansett Fire Department was called to the house, at 39 Marine Boulevard, at 1:43 a.m. on Friday. Chief Allen Bennett described the blaze as “a small deck fire.” The family inside was awakened by the smell of burning, Detective Schaeffer said. The homeowner and a police officer were able to extinguish the flames, he said. There was no significant damage.The house is the home of Carter Burwell, a composer of cinema scores who was nominated this winter for the score for “Carol,” and his wife, Christine Sciulli, an artist. Mr. Burwell is himself a volunteer firefighter. The couple declined to comment yesterday.“We don’t know if the family was targeted — I can’t answer yes or no,” Detective Schaeffer said.The East Hampton Town fire marshal’s office was called in, and it was after the fire marshal deemed it suspicious that police and arson investigators were notified, according to Chief Michael Sarlo.Tom Baker, a town fire marshal, referred all questions to arson detectives. Public information officers at the county police department said the arson squad had been called in to assist local police, and bounced questions back to the town force.It was not the only recent fire on that street, which is in the Beach Hampton neighborhood. On May 15, flames broke out at a house that was unoccupied and under construction, across the street from Mr. Burwell and Ms. Sciulli’s. That blaze, the Amagansett fire chief said, had begun in a dumpster four feet from the house and climbed up the side of the house. Despite strong winds, firefighters brought it quickly under control, though the second-story kitchen, several decks, a staircase, and parts of the roof were damaged.East Hampton Town Fire Marshal David Browne confirmed last week that the dumpster fire was not considered suspicious.