S.D. Codified Laws § 9-13-31
Current with legislation signed by the governor on or before 3/6/2024
The governing body shall, within ten days of presentation, order and fix a date for holding a special election, to be on a Tuesday not less than thirty nor more than fifty days from the date of the order of the governing body. If a petition is filed after December thirty-first before the annual municipal election and within sufficient time to comply with the provisions of § 9-13-14, the question of a successor shall be submitted at that annual election.
The governing body shall have a notice of election published in the same manner as provided in § 9-13-13.
SDCL 9-13-31