Kidd was charged with a misdemeanor of driving while intoxicated after a single-car accident in which his 2010 Cadillac Escalade struck a telephone pole and went into the woods in hamlet of Water Mill at around 2 a.m. Sunday.
The Southampton police told The New York Times that Kidd refused tests to measure the level of alcohol in his system. Kidd also declined a blood alcohol test at Southampton Hospital, according to the Times report.
"I had a few drinks," Kidd told the police, according to paperwork filed by the Southampton police for prosecutors that was obtained by the Times. "I was going home from a club. I don't know what happened."
Kidd is scheduled to appear in court on Sept. 12. He has pleaded not guilty to a charge of driving while intoxicated.
The veteran point guard also was charged with failure to stop and refusing a breathalyzer at the scene of the crash, charges his lawyer, Edward D. Burke Jr., told the Times were "traffic violations."