S.D. Codified Laws § 34-3-13
When two or more counties unite to form a full-time district health department a district board of health shall be created in the following manner: an appointing committee shall be formed, consisting of a representative of each governing board of each participating county and first or second class municipality, to be elected by such governing board. Counties and municipalities which become a part of such district after its initial formation shall have a representative on the appointing committee, to be selected in the same manner. Such committee shall appoint a district board of health consisting of five members, one of whom shall be a physician practicing in the district. When the number of counties and municipalities participating in the maintenance of such health department is five or less, then a qualified elector from each such participating county and municipality shall be appointed to the board.
SDCL 34-3-13