S.D. Codified Laws § 7-21-22
In the event of the passage and enactment of any law during a fiscal year and after the adoption of the annual budget for a following fiscal year, imposing some new obligation or duty upon a county, or in the event of the failure to provide by the final budget a sufficient revenue to enable the county to conduct the indispensable functions of government in any department, or to pay just obligations upon the county for the necessary conduct of the courts, or for the necessary aid and support of the poor or to discharge any duty which it is the lawful duty of the county to discharge, and of which requires the incurring of liabilities or expenditures of funds for a purpose or object for which no provision has been made in the annual budget for such fiscal year, and when such occasion arises the board must make, approve, and adopt a supplemental budget providing therein for an appropriation for such purposes in such amount as the board may deem necessary, and such budget shall set out in detail each item for which an appropriation is made and the amount thereof. Notice of its intention to make and adopt such supplemental budget, as provided in this section, stating the purpose, object and items and the amount to be appropriated for each item, with the time and place when the same will be considered and adopted by the governing board, shall be given in such manner as the board may determine, provided that the time fixed for considering and adopting the same shall not be less than ten days from date when such notice is first given.
SDCL 7-21-22