Wyo. Stat. § 27-10-106
Within five (5) days from the expiration of the thirty (30) day period referred to in W.S. 27-10-105, the bargaining agent and the corporate authorities shall each select and name one (1) arbitrator and shall immediately thereafter notify each other in writing of the name and address of the person so selected. The two (2) arbitrators so selected and named shall, within ten (10) days from and after the expiration of the five (5) day period hereinbefore mentioned, agree upon and select and name a third arbitrator. If on the expiration of the period allowed therefor the arbitrators are unable to agree upon the selection of a third arbitrator, a district judge of the judicial district within which the city is located, shall select him upon request in writing from either the bargaining agent or the corporate authorities. The third arbitrator, whether selected as a result of agreement between the two (2) arbitrators previously selected, or selected by a district judge, shall act as chairman of the arbitration board.
W.S. 27-10-106