An Arkansas contractor taking work in Oklahoma 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 Oklahoma's answer to each, with the agency's own link.
Licensing
Oklahoma Construction Industries Board (CIB)
No state general contractor license required; CIB licenses electrical, plumbing, mechanical/HVAC, and roofing contractors plus building and home inspectors; local jurisdictions may add registration and permit rules.
Workers compensation
Oklahoma Workers' Compensation Commission
Required for nearly all employers regardless of size; narrow exemptions include family-only businesses with five or fewer related employees and low-payroll agricultural employers.
Business registration
Oklahoma Secretary of State
https://oklahoma.gov/business/launch/register-your-business.html
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.