S.D. Codified Laws § 23-24A-25
From the time that a party state receives custody of a prisoner pursuant to this agreement until such prisoner is returned to the territory and custody of the sending state, the state in which the one or more untried indictments, informations, or complaints are pending or in which trial is being had shall be responsible for the prisoner and shall also pay all costs of transporting, caring for, keeping, and returning the prisoner. The provisions of this section shall govern unless the states concerned shall have entered into a supplementary agreement providing for a different allocation of costs and responsibilities as between or among themselves. Nothing herein contained shall be construed to alter or affect any internal relationship among the departments, agencies, and officers of and in the government of a party state, or between a party state and its subdivisions, as to the payment of costs, or responsibilities therefor.
SDCL 23-24A-25