S.D. Codified Laws § 34-3-5
Any municipality of the first class located within a county wherein a full-time county health department has been or is being established, may by mutual agreement between its governing body and the board of county commissioners of said county, merge its health service with such county department and participate in the financial maintenance of such county department to the extent of such agreement, and thereupon the county department shall have full supervision and control over all matters pertaining to public health in said municipality. Whenever a municipality of the first class shall merge with the county department, the mayor or member of the governing body of such municipality by it selected, shall become a member of the county board of health and shall be in addition to the members provided in § 34-3-3.
SDCL 34-3-5