S.D. Codified Laws § 34-10-12
The hospital district trustees elected for the first board shall serve for terms commencing upon their being elected and qualified and all trustees shall serve until their respective successors be elected and qualified. The term of office shall be for four years, except that the terms of the first board shall be so arranged so as to be overlapping, with three members serving until the next regular election; and four members until the second next regular election two years hence. The first board shall be elected at the same election held upon the creation of the district, subject to the creation thereof, shall qualify upon the organization of the district, if created, and the trustees may be nominated and have their names upon the ballots upon the filing with the board or boards of county commissioners of a petition signed by any five qualified electors of the district.
SDCL 34-10-12