An Arkansas contractor taking work in Texas 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 Texas's answer to each, with the agency's own link.
Licensing
No state general contractor license; Texas Department of Licensing and Regulation (electrical, HVAC) and Texas State Board of Plumbing Examiners (plumbing)
No statewide general contractor license; local rules apply. State licenses trades: electricians and air-conditioning/refrigeration contractors through TDLR; plumbers through the Texas State Board of Plumbing Examiners (tsbpe.texas.gov).
Workers compensation
Texas Department of Insurance, Division of Workers' Compensation
Optional for most private employers; building or construction employers contracting with governmental entities must provide coverage for employees on the public project.
Business registration
Texas Secretary of State, Business & Public Filings Division
Tax registration
Texas Comptroller of Public Accounts
Comptroller guidance: repair or remodeling of nonresidential real property is taxable on the entire charge; see Publication 94-105 for contract-type rules.
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
https://www.texasattorneygeneral.gov/child-support/employers/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.