S.D. Codified Laws § 12-21-43
When a tie vote between candidates is found to exist on the basis of any such recount, and by reason of such tie vote it cannot be determined who has been nominated or elected, it shall be the duty of the authority charged by law with the responsibility of issuing the certificate of election or nomination to fix a time and place for the drawing of lots by such candidates involved in such tie vote, giving reasonable notice of such time and place to each of such candidates. Each such candidate may appear at the time and place designated either in person or by a representative, whereupon in the presence of such authority charged with the responsibility of issuing the certificate of nomination or election, the candidate or candidates entitled to the certificate or certificates of nomination or election shall be determined by drawing of lots in the manner directed by such authority, and the certificate or certificates of nomination or election shall be issued accordingly.
SDCL 12-21-43