Bach, 44, was booked Monday afternoon and released about three hours later, according to Los Angeles County Sheriff's Department records. The actress is accused of backing her car into another vehicle on Jan. 22.
Bach's lawyer, Peter Knecht, has said Bach inspected both cars and left when she did not see any damage. An onlooker took down her license plate number.
Knecht did not immediately respond to a phone message left early Tuesday seeking additional comment.
Bach and Hasselhoff, who starred on the U.S. TV shows "Knight Rider" and "Baywatch," have been locked in a custody battle involving the couple's two teenage daughters.
The couple were married in December 1989. They divorced last year.