Wyo. Stat. § 1-36-105: When court to appoint arbitrators.

If the arbitration agreement provides a method of appointment of arbitrators this method shall be followed. In the absence thereof, or if the agreed method fails or for any reason cannot be followed, or when an arbitrator fails or is unable to act and his successor has not been appointed, the court on application of a party shall appoint one (1) or more arbitrators. An arbitrator so appointed has all the powers of one specifically named in the agreement.