S.D. Codified Laws § 9-13-14.2
The governing body of any municipality may, by ordinance enacted prior to the vacancy, require that any vacancy on the governing body or in the office of the mayor is to be filled by a special election called for that purpose to be conducted as provided in § 9-13-14 and this section. No special election may be held less than ninety days before the annual municipal election. The finance officer of the municipality shall publish a notice in the official newspaper of the municipality stating that a vacancy exists, that the vacancy will be filled by special election, the date of the election, and the time and place where nominating petitions may be filed for the office. The notice shall be published once each week for two consecutive weeks beginning at least sixty days before the date of the special election. Nominating petitions for the vacancy shall be prepared and filed as provided in § 9-13-7, may not be circulated more than sixty days before the date of the special election, and shall be filed at least thirty days before the date of the special election. The number of signers required for a nominating petition shall be calculated as provided in § 9-13-9. If a nominating petition is filed before the second Tuesday in January, the prior year's calculation of registered voters shall be used. A notice of the special election shall be published as provided in §§ 9-13-13 and 9-13-14.
SDCL 9-13-14.2