S.D. Codified Laws § 9-9-8
If the mayor is unable to perform the duties of office by reason of absence or sickness, the board shall appoint by a majority vote one of its members to act as mayor. The appointed commissioner's official designation shall be acting president of the board of commissioners. The acting president is invested with all the powers and shall perform all the duties of the mayor during the mayor's absence or sickness. The acting president has only one vote as a commissioner and is not entitled to vote as acting president.
If the office of mayor is vacated, the board of commissioners shall appoint by a majority vote one of its commissioners as acting mayor. The acting mayor is invested with all the powers and shall perform all the duties of the mayor, until the election of a mayor.
The acting mayor has only one vote as a commissioner and is not entitled to vote as acting mayor.
SDCL 9-9-8