Cal. Code of Civil Procedure § 1281.4

If a court of competent jurisdiction, whether in this State or not, has ordered arbitration of a controversy which is an issue involved in an action or proceeding pending before a court of this State, the court in which such action or proceeding is pending shall, upon motion of a party to such action or proceeding, stay the action or proceeding until an arbitration is had in accordance with the order to arbitrate or until such earlier time as the court specifies. If an application has been made to a court of competent jurisdiction, whether in this State or not, for an order to arbitrate a controversy which is an issue involved in an action or proceeding pending before a court of this State and such application is undetermined, the court in which such action or proceeding is pending shall, upon motion of a party to such action or proceeding, stay the action or proceeding until the application for an order to arbitrate is determined and, if arbitration of such controversy is ordered, until an arbitration is had in accordance with the order to arbitrate or until such earlier time as the court specifies. If the issue which is the controversy subject to arbitration is severable, the stay may be with respect to that issue only.