S.D. Codified Laws § 9-14-5
Each appointive municipal officer shall begin discharging the duties of the office as soon as the officer has qualified by filing an oath or affirmation of office in the usual form provided by law. The officer shall file the form within ten days after the first meeting of the month following the appointment. The officer shall hold office until the appointment and qualification of a successor.
Each elective municipal officer, if elected to fill a vacancy, shall begin discharging the duties of the office as soon as the officer has qualified by filing an oath or affirmation of office in the usual form provided by law. The officer shall file the form within ten days after the first meeting of the month following the election. Except as otherwise provided, each officer, if elected for a full term, shall begin discharging the duties of the office on the first meeting of the month next succeeding the election or as soon thereafter as the officer has qualified.
SDCL 9-14-5