Wyo. Stat. § 22-8-111: Acceptance of appointment.

With each notice of appointment delivered by the county clerk there shall be a form for acceptance of the appointment or notice that each appointee shall be required to notify the county clerk of acceptance. The county clerk shall state the date by which the appointee shall be required to notify the clerk of acceptance. Failure of an appointee to notify the county clerk of acceptance within the time allotted by the county clerk results in a vacancy.