Wyo. Stat. § 5-6-203
In all cases before the municipal court arising under ordinances of the city, wherein the fine assessed exceeds the sum of ten dollars ($10.00) or the imprisonment ten (10) days, an appeal may be taken by the defendant to the district court in and for the county in which the city is situated, but no appeal shall be allowed unless the defendant shall, within ten (10) days, enter into recognizance with sufficient sureties to be approved by the municipal court, conditioned for the payment of the fine and costs of appeal, and the defendant shall abide the judgment of the municipal court and not depart without leave of the court, or that he will pay to the city of ....the sum of $.....The procedure of the appeal shall be as prescribed for appeals from circuit courts in criminal cases.
W.S. 5-6-203