S.D. Codified Laws § 34-10-2
Whenever a petition praying that a public hospital district be established signed by not less than ten percent of the resident electors residing within the boundaries of the proposed public hospital district, which petition shall definitely describe the boundaries of the proposed district and request that the territory within said boundaries be organized into a public hospital district, shall be filed with the county auditor of the county within which said district is situated, and a duplicate thereof with the county auditor of each county where the district extends in more than one county; the same shall be presented by said county auditor or auditors to the board or boards of county commissioners at the first ensuing regular, adjourned, or special meeting of said board or boards. A petition for a popular vote on the question of issuing hospital bonds may be submitted at the same time or at a separate election after formation of the district. The petition for a bond issue election shall be subject to the same requirements as a petition for the creation of a hospital district.
SDCL 34-10-2