S.D. Codified Laws § 7-7-1.10
Current with legislation signed by the governor on or before 3/6/2024
If the offices are combined pursuant to § 7-7-1.2 and a vacancy occurs in one of the combined offices, the county commission shall appoint the remaining officer to hold the newly combined position until an officer can be nominated and elected.
SDCL 7-7-1.10