An Arkansas contractor taking work in New Mexico 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 New Mexico's answer to each, with the agency's own link.
Licensing
Construction Industries Division, NM Regulation and Licensing Department (CID/RLD)
CID licenses all contracting: a license is required to act, or offer to act, as a contractor (NMAC 14.6.3); no small-job dollar exemption appears in the licensing rule.
Workers compensation
New Mexico Workers' Compensation Administration
Required at three or more employees generally; every employer required to be licensed under the Construction Industries Licensing Act must carry coverage regardless of employee count.
Tax registration
New Mexico Taxation and Revenue Department
Gross receipts tax applies to services performed in New Mexico, construction included; combined state and local rate varies by location.
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.