S.D. Codified Laws § 46A-4-28
Subsequent to the election for organizing the district and for the first set of directors, the directors shall be nominated by filing with the auditor of the county or counties where the district is located, not less than forty-five days before any annual election, nominating petitions for the vacancies to be filled. The petitions shall be in the form prescribed by the State Board of Elections. To nominate directors by division, the petitions shall be signed by at least ten qualified electors of the district division or ten percent of the qualified electors of the division, whichever is less. To nominate directors at large, the petitions shall be signed by at least twenty-five qualified electors of the district or ten percent of the qualified electors of the district, whichever is less. No petition may contain the name of more than one candidate for any vacancy to be filled, but each elector may sign as many petitions as there are directors to be elected and no elector may sign more than one petition for any particular vacancy.
SDCL 46A-4-28