S.D. Codified Laws § 34-3-27
Any county or first or second class municipality participating in a full-time district health department may withdraw from the department and board by resolution of its governing board providing no such withdrawal may occur within one year of the date of establishment of the department or the date of entrance of said county or municipality into said department. It is further provided that no withdrawal shall occur during any fiscal year for which a budget has been approved and in no instance until ninety days' prior written notice of such withdrawal has been given to the district board of health.
When a participating county or municipality withdraws from a district health department its representative on the appointing committee shall also withdraw therefrom and any positions held by its representatives on the district board of health shall be declared vacant and the vacancy or vacancies so created shall be filled as provided in § 34-3-3.
SDCL 34-3-27