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.
Representatives of the Israeli Defence Ministry responded to recent reports about the possible delivery of S-300 SAM systems from Russia to Syria. Israeli Defence Minister Avigdor Lieberman said that Israel would destroy those systems
Russia is to start supplying S-300 air defence systems to Syria in the near future. The shipments will be conducted free of charge