S.D. Codified Laws § 27A-14-5
If the county board fails or neglects to take and remove such patient so discharged, as provided in § 27A-14-3, within forty-eight hours from the date of the order discharging him and of the notice of the order, the responsible county is liable for and shall pay to the state full service cost as such term is defined in § 27A-13-2 for the care and keeping of such patient at the center or facility, the time of such keeping to be computed and commence forty-eight hours after the date of such order and notice.
The administrator or other director shall report any such delinquencies, and the time any patient is so kept beyond such time aforesaid, giving his name, the county where he belongs, and the amount due from such county for such charge, to the state auditor who shall notify the county auditor of the county to be charged, and the same shall be paid into the state treasury as other charges for the support of the mentally ill.
SDCL 27A-14-5