An Arkansas contractor taking work in Maine 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 Maine's answer to each, with the agency's own link.
Licensing
Office of Professional and Occupational Regulation (OPOR)
No state general-contractor license. Electricians and plumbers are licensed by state examining boards under OPOR; boiler, elevator, and architect programs also state-run. General home-construction contracting is otherwise unlicensed at state level.
Workers compensation
Maine Workers' Compensation Board
Nearly all public and private employers must carry coverage; limited exemptions for domestic servants and certain agricultural or aquacultural employers carrying liability insurance.
Business registration
Maine Secretary of State, Bureau of Corporations, Elections & Commissions
https://www.maine.gov/sos/corporations-commissions/corporations-business-services
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.