S.D. Codified Laws § 61-6-66
No individual may receive extended benefits for any week of unemployment in the individual's eligibility period if the secretary finds that during the period the individual failed to accept an offer of suitable work, failed to apply for suitable work to which the individual was referred by the secretary, or failed to actively engage in seeking work.
An individual who has been found to be ineligible for extended benefits shall be denied benefits for the week in which the failure occurred and until the individual has been subsequently employed for at least six calendar weeks in insured employment and has earned wages of not less than the individual's weekly benefit amount in each of those six weeks.
The term, suitable work, in this section means any work within an individual's capabilities which has a gross weekly wage that exceeds the individual's weekly benefit amount plus any supplemental unemployment benefits and which pays not less than the higher of the federal minimum wage as provided by the Fair Labor Standards Act or the state minimum wage.
No individual may be denied extended benefits for failure to accept an offer of, or apply for, a job which would otherwise be suitable work if:
An individual is actively seeking work during a week if the individual engages in a sustained and systematic effort to obtain work during that week and the individual furnishes tangible evidence that the individual has engaged in such an effort during that week.
The department shall refer an individual who is entitled to extended benefits to any suitable work which meets the criteria described in this section.
SDCL 61-6-66