S.D. Codified Laws § 23A-6-19
If trial has not commenced, a prosecuting attorney may amend an information to allege, or to change the allegations regarding, any offense arising out of the same alleged conduct of the defendant that gave rise to any offense alleged in the original information. If the change alleges a new offense, the defendant has the right to a preliminary hearing on the new offense.
After commencement of a trial, the trial court may permit the prosecuting attorney to amend the information at any time before a verdict or finding is made, if no additional or different offense is charged and substantial rights of the defendant are not thereby prejudiced. An amendment may charge an additional or different offense with the express consent of the defendant.
SDCL 23A-6-19