S.D. Codified Laws § 3-4-9
If any member of a governing body or any other elected officer of a county, municipality, school district, township, or special purpose district, who is incapacitated by illness or an accident which causes the member or officer to be unable to attend meetings of the governing body or fulfill the duties of the office, the member may elect to temporarily resign from the governing body or office. Notice of temporary resignation may be given in the same manner as giving notice of resignation from the governing body or office. If the member or officer is unable to give notice, the member's or officer's spouse or guardian or any person who has durable power of attorney for the member or officer may give notice of resignation. A temporary replacement may be made in accordance with the provisions of statute applying to the governing body or office. The temporary member or officer shall serve until the member or officer is able to fulfill the requirements of office or until the expiration of the member's or officer's term, whichever comes first.
SDCL 3-4-9