S.D. Codified Laws § 7-3-2
If a majority of the votes cast at the next general election in such county, and also in each portion thereof proposed to be organized into a new county, shall be favorable to a division of such county, the portion in which the county seat thereof is located shall retain the name and organization of such county and the portion or portions in which the county seat is not located shall take the name or names prayed for in the petition for the division of the county, and the Governor shall forthwith proceed to organize the same as a county or counties under such name or names in the manner provided by law for organizing an unorganized county and, until such organization is perfected, the said portion or portions of such county shall for all governmental purposes remain and be a portion of such original county.
SDCL 7-3-2