Colorado does not license general contractors at state level. There is no state licence to look up and no state register that will confirm one. General contracting is licensed city by city — Denver, Colorado Springs, Aurora and the rest each run their own registration, with their own classes and their own exams — and none of them publishes that register as open data, so none of it is verifiable through any API.
Try a free lookup — no signup, right here on this page. For programmatic access, take a free API key — 250 requests a month, no card. Also on RapidAPI and, if you would rather not write code at all, the Apify Store.
What is verifiable: the electrical and plumbing work on the job. Colorado requires those trades to be licensed by the state, and this API checks them in one call. Ask a general contractor which city they are registered in and check it with that city directly, then verify the trades separately here — that is the whole of what can actually be confirmed in Colorado.
Full coverage detail, including the caveats that apply to every Colorado lookup, is on the Colorado page.
The API is on RapidAPI with a free tier: Contractor License Verification. It is also on the Apify Store: Contractor License Lookup & Verification. Full schema at /docs.