If the offices of governor and lieutenant governor be both vacant by reason of death, resignation, impeachment, or inability to serve, the speaker of the house of representatives shall in like manner fill the office of governor during such vacancy.
S.D. Const. art. IX, § 10 — under County and Municipal Corporations.
S.D. Const. art. IX, § 10
Vacancies in Both Offices of Governor and Lieutenant Governor
If the offices of governor and lieutenant governor be both vacant by reason of death, resignation, impeachment, or inability to serve, the speaker of the house of representatives shall in like manner fill the office of governor during such vacancy.