Wyo. Stat. § 22-5-215
On each party ballot the candidate or candidates equal in number to the number to be elected to each office who receive the largest number of votes shall be nominated and shall be entitled to have their names printed on the ballot for the next general election. A write-in candidate shall not be nominated and shall not be entitled to have his name printed on the ballot for the next general election unless he received at least twenty-five (25) write-in votes in the primary election and is a registered voter in the political party for which he was nominated on the day of the primary election. An unsuccessful candidate for office at a primary election whose name is printed on any party ballot may not accept nomination for the same office at the next general election.
W.S. 22-5-215