S.D. Codified Laws § 12-1-37
If the random sample required by § 12-1-36 indicates that a sufficient number of qualified electors have signed the nominating petition for statewide office, the secretary of state shall certify that the nominating petition for statewide office has been signed by the required number of qualified electors and shall place the candidate's name on the next primary or general election ballot, as the case may be.
If the random sample indicates that an insufficient number of qualified electors have signed the nominating petition for statewide office, the secretary of state shall certify that the nominating petition for statewide office has not been signed by the required number of qualified electors and may not place the candidate's name on the next primary or general election ballot, as the case may be.
The secretary of state shall, within five days of certifying, notify the candidate of the secretary of state's action pursuant to this section.
SDCL 12-1-37