Wyo. Stat. § 38-2-106
Any surety upon the bond of any state, county or municipal officer shall be released from further liability of such surety for such officer, by filing with the person or persons having authority to approve said bond, or with whom said bond is directed to be filed, a notice that said surety is unwilling longer to be security for such state, county or municipal officer. When any notice shall be filed as aforesaid, notice thereof shall immediately be given to such state, county or municipal officer, who shall thereupon file within fifteen (15) days other security to be approved as provided by law. If said state, county or municipal officer shall not in the manner aforesaid file such bond to be approved as aforesaid, the said office shall become vacant and the said vacancy shall be filled in manner as is now provided by law. If a new bond shall be given by any officer, as hereinbefore provided, then the former surety or sureties shall be entirely released and discharged from all liability incurred by such officer after the time of the approval of said new bond, and the sureties to the new bond shall henceforth be liable as therein provided, after the approval of said new bond as aforesaid. The officer, officers, board or official body where or with whom said original bond was filed, shall have power to declare any office or offices vacant as hereinbefore provided; provided, that no surety shall be released from further responsibility until the office shall be declared vacant or a new bond approved by the proper authority.
W.S. 38-2-106