The state Attorney General’s Office has refused to release the identity of the man who was shot dead by Jersey City police late Tuesday night, citing the “ongoing” investigation. The man was shot at the corner of Communipaw and West Side avenues at approximately 11:56 p.m. by officers who were responding to a call of a domestic violence incident involving a man with a gun. The AG’s Office said in a statement Wednesday that “during the encounter” one Jersey City police shot and killed the man and a gun was found near his body. The man was pronounced dead at the scene at 12:19 a.m. “The investig…