S.D. Codified Laws § 12-21-14
Whenever any referred or submitted question is voted upon throughout the state and is determined according to the official canvass by a margin of not exceeding one-fourth of one percent of the total vote cast for and against on such question, there may be filed with the secretary of state within ten days after the completion of the official canvass by the State Board of Canvassers a petition signed by not less than one thousand registered voters of the state, and representing at least five counties of the state, setting forth that petitioners believe a recount will change the result and praying that such recount shall be had in all the precincts involved. Such petition may consist of different petitions bound together and signed and verified substantially as provided by law with regard to petitions to invoke the referendum. Upon the filing of such petition, the secretary of state shall forthwith by registered or certified mail notify each county auditor whose county voted upon the question and such recount shall then be conducted in all of the precincts in each of such counties.
SDCL 12-21-14