S.D. Codified Laws § 8-4-11
If any township fails to elect any township officer, or if any person elected to an office fails to qualify by refusing to serve in such office or by not being a registered voter or by not having residence in the township, or if any vacancy happens in any office from death, resignation, removal from the township, or other cause, the board of supervisors, or a majority of them, shall fill the vacancy by appointment, by warrant under their hands. Any person so appointed shall hold his office until the next annual township meeting and until his successor has been elected and qualified. Such person shall have the same power and be subject to the same duties and penalties as if he had been duly elected. The township clerk according to § 8-6-6 shall prescribe the oath or affirmation of office required by § 3-1-5 and require the person so appointed to qualify pursuant to §§ 8-4-3 and 8-4-4.
SDCL 8-4-11