SDCL § 3-4-4: Board of county commissioners--Filling vacancies.

When a vacancy occurs in the board of county commissioners, the remaining board members must appoint a suitable person to fill the vacancy from the district where the vacancy occurs. The board has thirty-five days to fill the vacancy or until the conclusion of the second regular meeting after the vacancy occurs, whichever is later. If there is an even number of county commissioners remaining on the board, the county auditor must act as a member of the board to fill the vacancy.