Whenever according to the official returns as publicly announced and compiled, although not yet officially canvassed, it fairly appears that one group of candidates for presidential electors has been elected over another group of such candidates by a margin not exceeding one–fourth of one percent of the total of votes cast for both such groups, the chairman of the state central committee of the political party which nominated either of such groups, or any two or more candidates of either such group, may file with the secretary of state at any time after the election and prior to the canvass by the State Board of Canvassers, a petition setting forth that in the opinion of the petitioner or petitioners all votes cast for presidential electors should be recounted. Upon the filing of such petition, the secretary of state shall forthwith by registered or certified mail notify each county auditor in the state thereof, and such recount shall then be conducted in all of the precincts in all of such counties.

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Source: SDC 1939, § 16.1803 (6).