An Arkansas contractor taking work in Nebraska 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 Nebraska's answer to each, with the agency's own link.
Licensing
Nebraska Department of Labor (Contractor Registration)
No statewide GC license. Under the Contractor Registration Act, all contractors and subcontractors engaging in work on real property other than their own must register with the Nebraska Department of Labor; registrants with employees must file a current workers' compensation insurance certificate.
Workers compensation
Nebraska Workers' Compensation Court
Applies to every resident or nonresident employer with one or more employees; agriculture (under ten unrelated full-time employees), domestic service and railroads exempt (Neb. Rev. Stat. 48-106).
Tax registration
Nebraska Department of Revenue
DOR publishes Nebraska Taxation of Contractors Option 1, 2 and 3 guidance for construction contractors.
https://revenue.nebraska.gov/businesses/register-your-new-business-online
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.