Wyo. Stat. § 24-1-114
Whenever it shall appear to be advantageous to any county or counties to build or repair any bridge or bridges over streams constituting the boundary line of such county or counties, or when such bridge or bridges when built will be partly in one (1) county and partly in another county in this state, or when a bridge when built shall be partly in a county of this state and partly in a county of another state, it shall be lawful for the county commissioners of any county in which part of such bridge has been or is to be erected, to join with the other county or counties containing or to contain other parts of the said bridge, in making any contract or contracts for the purpose of procuring the erection or repair of such bridge or bridges on the basis that each of the counties contracting shall pay one-half of the whole expense of building or repairing such bridge or bridges.
W.S. 24-1-114