S.D. Codified Laws § 12-21-37

If such corrected abstract by the county recount board shows no change in the result as previously found on the official returns, no further action shall be taken. But if there is a change in such result, a new certificate of election or nomination shall be issued to each candidate found to have been elected or nominated as the case may be, which certificate shall be signed by at least two members of such board, and shall set forth the nomination or election of such person as to such office or position.