S.D. Codified Laws § 12-21-11
If any legislative district comprises more than one county, any candidate for election to or nomination for the Legislature who, according to the official returns, has been defeated by a margin not exceeding two percent of the total vote cast for all candidates for such office may, within three days after completion of the official canvass of the returns, file a petition as set forth in § 12-21-10 with the county auditor of each county. Each county auditor shall then conduct a recount.
Notwithstanding § 12-21-20, if the recount is for a legislative district comprising more than one county and the candidate expresses to the county auditor in writing to be present at each county's recount, the board shall convene at the time and date determined by mutual agreement between the county auditor and candidate. All such recounts shall be completed within fourteen days following the filing of the petition.
SDCL 12-21-11