S.D. Codified Laws § 9-13-26.1
If a municipality has passed an ordinance requiring a runoff election, and no candidate in a race involving three or more candidates receives a majority of the votes cast in the race, a runoff election shall be held three weeks from the date of the first 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. However, if there is a tie for second place in the first election and there is no tie for first place, all tying second place candidates shall be placed along with the first place candidate on the ballot for the runoff election. The runoff election shall be held at the same polling places and shall be conducted, returned, and canvassed in the same manner as the first election. The result shall be declared and entered in the minutes of the municipality in the same manner as the first election. The person receiving the highest number of votes at the runoff election is elected.
SDCL 9-13-26.1