CA Civ Proc Code Section 1281.12

If an arbitration agreement requires that arbitration of a controversy be demanded or initiated by a party to the arbitration agreement within a period of time, the commencement of a civil action by that party based upon that controversy, within that period of time, shall toll the applicable time limitations contained in the arbitration agreement with respect to that controversy, from the date the civil action is commenced until 30 days after a final determination by the court that the party is required to arbitrate the controversy, or 30 days after the final termination of the civil action that was commenced and initiated the tolling, whichever date occurs first.