Wyo. Stat. § 9-1-212
Whenever the powers and duties of the office of the governor of the state of Wyoming devolve upon any other person as provided in W.S. 9-1-211(a), the person acting as governor shall continue to act as governor until the end of the term of the governor if the office is assumed less than sixty (60) days before the next general election. If the office is assumed more than sixty (60) days before a general election the person acting as governor shall issue an additional proclamation calling for the election of a governor to fill the unexpired term, which election shall take place at the same time as the general election, and the election, together with the returns and canvass thereof, shall be conducted in all respects as though it was an original election for governor. When the state canvassing board canvasses the vote of the election and declares a person at the election to be elected as governor, the person shall, within thirty (30) days after the canvass, or as soon thereafter as possible, qualify and assume the duties and powers of governor, and shall be the governor of the state of Wyoming for the remainder of the unexpired term of the governor.
W.S. 9-1-212