An Arkansas contractor taking work in Washington 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 Washington's answer to each, with the agency's own link.
Licensing
Washington State Department of Labor & Industries (L&I)
Registration, not an exam-based license: all construction contractors register with L&I, with surety bond ($30,000 general, $15,000 specialty), liability insurance, and a $150.20 fee; no exam, though plumbing and electrical trades have separate exam-based licensing.
https://lni.wa.gov/licensing-permits/contractors/register-as-a-contractor/
Workers compensation
Washington State Department of Labor & Industries
Monopolistic: private workers' comp coverage not allowed; employers with workers must buy coverage through L&I (or qualify as certified self-insured), paying quarterly premiums based on worker hours.
https://www.lni.wa.gov/insurance/insurance-requirements/do-i-need-a-workers-comp-account/
Business registration
Washington Secretary of State, Corporations & Charities Division
Tax registration
Washington Department of Revenue
B&O gross receipts tax applies; construction businesses may owe under multiple B&O classifications.
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
https://www.dshs.wa.gov/esa/division-child-support/new-hire-reporting
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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.