S.D. Codified Laws § 34-8-7
To manage or assist them in the management of a county hospital, the board of county commissioners may appoint a board of trustees consisting of five competent and responsible freeholders of the county, one of whom shall be a legally qualified physician or nurse, in which case one member of said board shall be appointed for a term of one year, one for a term of two years, one for a term of three years, one for a term of four years, and one for a term of five years.
Their terms of office shall expire on the first Monday of July of the year of expiration. Thereafter it shall be the duty of such board of county commissioners annually at their regular meeting in July to appoint for a term of five years a successor to the trustee whose term of office shall expire during that year.
Any member of such board of trustees may be removed at any time by the board of county commissioners.
SDCL 34-8-7