Every motor vehicle dealer, repairer, leasing company, and manufacturer operating in the state of Connecticut must be licensed by the Department of Motor Vehicles.
The list of those licensed by the state to operate updates weekly and can be found at the DMV website. Any place not on this list is not a reputable location and you are using them at your own risk.
If you have an issue with a repair shop or other kind of company on this list, the DMV has authority to investigate some but not all issues. A list of these issues can be found here. You can also find a form to file a complaint against a company on the list of licensed companies.