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He pleaded not guilty to the misdemeanor, his lawyer said.
Kidd, a 10-time all-star who recently signed with the New York Knicks, was treated for minor injuries at the hospital and released from custody on his own recognizance, police said.
Southampton Town Police reported receiving a call shortly before 2 a.m. about a car that struck a telephone pole and went into the woods.
"Police responded to the scene and found the driver of the vehicle, Jason Kidd, age 39 of Dallas, Texas, to be intoxicated," police said in a statement. "It was a single car accident in which Mr. Kidd was the single occupant of the 2010 Cadillac Escalade."
Eddie Burke Jr., a lawyer representing Kidd, said his client pleaded not guilty at an arraignment on Sunday. Burke declined to comment on Kidd's injuries and said he was awaiting further evidence from the investigation ahead of a September court date.
"(Kidd) is doing OK," Burke said. "He was released on his own recognizance and has to come back to court in September."