Dino Tomassetti, 29, was arrested in New Jersey the same day as the shooting, after the Brooklyn resident was tracked to Mahwah.
He was extradited back to Nassau County and is charged with two counts of second-degree murder.
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Police say the Christmas morning dispute ended with Tomassetti shooting 64-year-old Vincenza Tomassetti in the head and 65-year-old Rocco Tomassetti in the back inside their multi-million dollar home on Seawane Drive in Hewlett Harbor.
Authorities say he also beat his father over the head with the gun after he ran out of bullets.
The dispute was apparently based on the custody of Dino Tomassetti's 1-year-old child with his wife, from whom he is separated, and apparently dispute escalated when Dino attempted to take the child.
"It had to do with custody and taking the child," Nassau County Police Commissioner Patrick Ryder said. "It's Christmas morning. The man wanted to take his 1-year-old away from parents and the natural mother, which he did not have custody to. And there's where the argument started."
Both the child and the child's mother were in the room when the shooting happened. Police said they were not physically injured.
The parents survived, and both have been released from the hospital and are recovering.
The child remains with the mother.
Rocco Tomassetti reportedly heads a construction company.
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