S.D. Codified Laws § 13-6-75
If a majority of the school board members reside in that portion of an existing school district which is transferred to another school district as a result of an election on a school district reorganization plan, these vacancies shall be filled by an election conducted by the school board and held prior to the first Monday in May as provided in § 13-6-64. If less than a majority of the school board members reside in that portion of an existing school district which is transferred to another school district as a result of an election on a school district reorganization plan, these vacancies shall be filled by appointment by the remaining members of the board until the next regular school board election, and such appointments shall coincide with the time limits provided in § 13-6-64.
SDCL 13-6-75