Henderson’s vehicle was towed from the scene and he was transported to the Parker County Jail, where he posted $1,000 on the class B misdemeanor charge later that morning, according to jail records.
Halstead said Henderson has been placed on “reduced status” following the off-duty arrest.
Halstead said in a statement that the matter is being investigated both criminally and administratively, limiting how much he could comment.
But he confirmed that Henderson “was assigned as my chief of staff,” and said he’d “make immediate changes in his responsibilities.”
Halstead said Henderson had apologized.
The police chief added: “I fully expect our employees, my supervisors, and, most importantly, our citizens, to hold me accountable as I address this misconduct with fairness and professionalism.”
Associated Press contributed to this story.