Wyo. Stat. § 28-1-106: Resignation of office.

Resignation of the office of a member of the senate or house of representatives shall be made to the governor, who shall immediately notify the state central committee of the party which the member represented at the time of his election under W.S. 22-6-120(a)(vii), or at the time of his appointment if not elected to office, of the resignation. If the resigning member did not represent a political party at the time of his election, or at the time of his appointment if not elected to office, the governor shall notify the appropriate boards of county commissioners who shall proceed in accordance with W.S. 22-18-111(a)(iii)(C). For purposes of this section a person shall be considered to "represent" a political party if he was a nominee of that political party when elected to office or when appointed to fill a vacancy in office.