S.D. Codified Laws § 12-6-51.1
If no candidate for United States Senate, United States House of Representatives, or Governor in a race involving three or more candidates receives thirty-five percent of the votes of the candidate's party, a runoff election shall be held eight weeks from the date of the first primary election. At the runoff election the only persons voted for shall be the two candidates receiving the highest number of votes at the first election. If there is a tie for second place in the first primary election and there is no tie for first place, all tying second place candidates must be placed along with the first place candidate on the ballot for the runoff election. The runoff election must be held in the same manner as the first election. However, if the runoff election does not have a federal race, the electronic ballot marking system is not required, and hand-counted ballots may be used. The person receiving the highest number of votes at the runoff election is nominated as the candidate for the party.
SDCL 12-6-51.1