S.D. Codified Laws § 28-14-2.1
If a county furnishes relief under the provisions of chapter 28-13 to any person who has been a resident of the county as determined by chapter 28-13 for less than sixty days prior to the making of an application for nonemergency hospitalization assistance as provided by § 28-13-34.1 or his being hospitalized in an emergency situation, and the county is unable to collect the amount of the relief furnished from the person receiving the relief, the county which furnishes the relief shall have a claim for reimbursement against the county of which the person was a resident sixty days prior to application for hospitalization assistance or the emergency hospitalization. The county which furnishes the relief shall give notice of the claim for reimbursement to the county auditor of the county of which the person was last a resident. The county of which the person was last a resident shall make the reimbursement out of the poor relief funds for that county.
SDCL 28-14-2.1