S.D. Codified Laws § 7-21-10
At any meeting held pursuant to § 7-21-9 and during the consideration of the provisional budget by the board, the board may eliminate, amend, correct, change, or alter any of the purposes, objects, items, schedules, appropriations, amounts, estimates, or matters contained in the provisional budget in such manner as the board may deem necessary and proper. All such amendments, eliminations, corrections, changes, alterations, insertions, and additions shall be made before the final approval and adoption of the budget by the board before October first of each year. All amendments, corrections, changes, alterations, eliminations, insertions, and additions made in or to the provisional budget shall be noted on the provisional budget and shall be entered at length in the minutes of the board.
SDCL 7-21-10