An Arkansas contractor taking work in Wisconsin 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 Wisconsin's answer to each, with the agency's own link.
Licensing
Wisconsin Department of Safety and Professional Services (DSPS)
No statewide general contractor license. To obtain building permits for one- and two-family dwellings, a business must hold a DSPS Dwelling Contractor certification and hold or employ a certified Dwelling Contractor Qualifier (12-hour initial course); apply via license.wi.gov.
https://dsps.wi.gov/Pages/Professions/DwellingContractor/Default.aspx
Workers compensation
Wisconsin Department of Workforce Development, Worker's Compensation Division
Required with three or more employees, or once one or more employees are paid $500 or more in combined gross wages in a calendar quarter; farmers at six or more workers on 20 days.
Business registration
Wisconsin Department of Financial Institutions (DFI handles business filings, not the Secretary of State)
https://dfi.wi.gov/Pages/BusinessServices/BusinessEntities/FileOnline.aspx
Tax registration
Wisconsin Department of Revenue
https://www.revenue.wi.gov/Pages/Businesses/New-Business-home.aspx
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.