S.D. Codified Laws § 12-21-16
Whenever by reason of a tie vote found to exist upon the canvass of the original official returns, it is impossible to declare who has been elected or nominated to an office or position, it shall thereupon be the duty of the official board making such canvass to certify said vote to the county auditor where the election involved is confined to or within the limits of a county, and to the secretary of state as to all other elections. Thereupon such county auditor or such secretary of state, as the case may be, shall proceed exactly as if a petition had been duly filed under §§ 12-21-7 to 12-21-15, inclusive, requiring a recount to be made of all votes involved, and such recount shall proceed accordingly. This section shall not apply to school and township elections.
SDCL 12-21-16