An Arkansas contractor taking work in South Dakota deals with the same four questions everywhere: who licenses the trade, when a licence is actually required, when workers compensation kicks in, and where the business registers. Below is South Dakota's answer to each, with the agency's own link.
Licensing
SD Electrical Commission and State Plumbing Commission (Dept. of Labor & Regulation); Dept. of Revenue for contractor tax license
No statewide general-contractor license or board; DLR's board list includes only Electrical and Plumbing commissions for construction trades. Every construction contractor must instead hold a Department of Revenue contractor's excise tax license.
Workers compensation
SD Dept. of Labor & Regulation, Division of Labor & Management
Not mandatory: no law in South Dakota requires any employer to carry workers' compensation insurance, but uninsured employers face civil suits; coverage strongly advised.
Business registration
South Dakota Secretary of State
https://sosenterprise.sd.gov/BusinessServices/Business/RegistrationInstr.aspx
Tax registration
South Dakota Department of Revenue
2 percent contractor's excise tax on gross receipts; anyone contracting construction services must hold a contractor's tax license.
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
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Starting or running the business itself is covered in the contractor business guide. Arkansas licence records for Benton and Washington counties are in the contractor directory.