S.D. Codified Laws § 49-35-17
A petition for the annexation of additional territory to an existing district may be filed by registered voters of the area to be annexed. Petitions for the consolidation of two or more existing districts shall be filed by registered voters of each existing district. These petitions shall be filed with the secretary of state, specifying the territory to be annexed or the districts to be consolidated, in accordance with the provisions of §§ 49-35-7 to 49-35-9, inclusive. Upon the filing of such petition, the secretary of state shall follow the procedures of § 49-35-10, and an election shall be held pursuant to the provisions of this chapter. If the majority of the electors of such additional territory or in each of the districts to be consolidated, as the case may be, voting thereon shall vote in favor of such annexation or consolidation, the county auditor or municipal finance officer, as the case may be, shall file the results of such election in the principal places of business of the existing districts involved.
SDCL 49-35-17