S.D. Codified Laws § 3-4-6
Appointments to state offices shall be made in writing and shall continue for the remainder of the unexpired term of office. Unless otherwise provided by law, all other appointments shall be made in writing and shall continue until the next general election and until a successor is elected and qualified. A vacancy must occur prior to May first in an even-numbered year, other than in a year when the term of office would normally expire, for the office to be filled by election for the remainder of the unexpired term. Any person elected to an office that was previously vacant shall take office in the year following the election on the day of that year when a full term for that office would normally commence.
Appointments to state offices shall be filed with the secretary of state. Appointments to county offices shall be filed in the office of the county auditor and entered in the minutes of the commissioners' proceedings.
SDCL 3-4-6