Wyo. Stat. § 18-3-106
Each county clerk, county treasurer, clerk of the district court, county assessor and county sheriff shall devote full time to the duties of their respective offices during the term for which they were elected or appointed. In counties which are not served by a district attorney and in which the population exceeds nine thousand (9,000) but is less than sixty thousand (60,000), the county and prosecuting attorney shall devote full-time to the duties of his office whenever a majority of the county commissioners in that county resolve that a full-time county and prosecuting attorney is necessary. In counties which are not served by a district attorney and in which the population does not exceed nine thousand (9,000), as well as in counties which are served by a district attorney, the county commissioners may designate the office of county attorney and the office of county and prosecuting attorney as a full-time office. The designations shall be made by resolution at the time salaries are set under W.S. 18-3-107(a).
W.S. 18-3-106