S.D. Codified Laws § 28-13-33
Subject to the provisions of this chapter and except as expressly provided, if a hospital furnishes emergency hospital services to a medically indigent person, the county where the medically indigent person has established residency is liable to the hospital for the reimbursement of the hospitalization. In the case of nonemergency care, the county of residence is liable only to the extent that the board of county commissioners, in good faith, approves an application for assistance. If a county provides payment for nonemergency services, the services shall be approved by the county before the services are provided. To the extent that the county provides payment to a hospital, the county has the same remedies for the recovery of the expense as are provided by chapter 28-14 for the recovery of money expended for the relief and support of poor and indigent persons.
SDCL 28-13-33