As Ensoluna recommends, you will need to check with your state authorities. I am in the process of starting up (my roaster is currently making its way across the Pacific Ocean).
In New York, food preparation falls under either Farms and Markets or NY Health Dept. Coffee roasting does not fall under the home kitchen exemption, like baked goods do. Farms and Markets is a bit less strict than Health Dept in NY. The difference in authority is how much of your business is retail (e.g. bagged roasted beans, coffee making paraphernalia, t-shirts, etc.) and on-site service (e.g. serving coffee drinks, pastries, etc.).
At a minimum, in NY, you are required to have a commercial kitchen with three-basin sink, hand-washing station, and washable floors, walls, ceiling. I would not be at all surprised to find the same in CT. A little time spent on a search engine should help elucidate this.
Best of luck with your venture!
Regards,
Dan
Gato Diablo Coffee (and maybe Chocolate).