An Arkansas contractor taking work in New York 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 York's answer to each, with the agency's own link.
Licensing
No statewide contractor licensing agency; local licensing (e.g., NYC Department of Consumer and Worker Protection)
No statewide contractor license; NYS DOS confirms New York State does not license home improvement contractors. Some counties and cities do, including NYC, Buffalo, Nassau, Suffolk, Westchester, Putnam, Rockland. NYC requires a DCWP Home Improvement Contractor license for residential work.
https://www.nyc.gov/site/dca/businesses/license-checklist-home-improvement-contractor.page
Workers compensation
New York State Workers' Compensation Board
Virtually all employers must provide coverage for anyone working for them; sole proprietors and partnerships without employees are exempt (WCL sections 2 and 3).
https://www.wcb.ny.gov/content/main/coverage-requirements-wc/wc-coverage-required.jsp
Business registration
New York Department of State, Division of Corporations, State Records and Uniform Commercial Code
Tax registration
New York State Department of Taxation and Finance
New hire reporting
Most states require newly hired employees to be reported within a short window of their start date.
New Mexico · All fifty states · North Carolina
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.