Lt. Anne Ralston says Martin was with two adults and two juveniles and also was charged with child endangerment.
Martin says in a Monday statement that he takes the matter seriously and intends to vindicate himself in court.
According to a tweet on his Twitter account, Martin in May rode along with state and local police in Beavercreek setting up a drunken driving checkpoint.
A fellow GOP legislator, state Rep. Robert Mecklenborg, resigned July 17 after a drunken driving charge in Indiana.