An Arkansas contractor taking work in Idaho 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 Idaho's answer to each, with the agency's own link.
Licensing
Idaho Contractors Board, Division of Occupational and Professional Licenses (DOPL)
State registration with the Idaho Contractors Board (DOPL) rather than a competency license; $50 fee, biennial renewal; statute exempts projects under $2,000 aggregate; electrical, plumbing, and HVAC are licensed separately by DOPL boards.
Workers compensation
Idaho Industrial Commission
Employers with one or more full-time, part-time, seasonal, or occasional employees must carry workers' comp before hiring unless specifically exempt; policies from licensed carriers, overseen by the Industrial Commission.
Tax registration
Idaho State Tax Commission
Contractors are consumers: they pay sales and use tax on materials, equipment, and supplies used improving real property.
https://tax.idaho.gov/online-services/business-registration/
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.