S.D. Codified Laws § 12-21-12
If any candidate for an office, position, or nomination other than the Legislature is voted upon in more than one county, and has been defeated according to the official returns by a margin which does not exceed one-fourth of one percent of the total vote cast for all candidates for such office, position, or nomination, the candidate may within three days after completion of the official canvass by the State Board of Canvassers file a petition with the secretary of state setting forth that the candidate believes a recount will change the result and that all of the votes cast for the office, position, or nomination should be recounted. The secretary of state shall, by registered or certified mail, notify each county auditor that has precincts included in the petition. Each county auditor shall then conduct a recount.
SDCL 12-21-12