Wyo. Stat. Ann. § 22-5-212

An elector requesting a major party ballot shall declare or change party affiliation in accordance with W.S. 22-5-214 before receiving a party ballot. An elector may vote only the nonpartisan ballot and if so, is not required to declare his party affiliation. Requesting a partisan primary election ballot constitutes a declaration of party affiliation. A change in declaration of party affiliation shall be in accordance with the requirements of W.S. 22-5-214 and shall be entered on the poll list by the election judge.