In CT you have to take the NRA certification. Get that cert, have it!

Once you have that, you go to your town's main PD or town clerk, depends on how small your town is. You ask them where to apply. You go to that clerk/desk, you get the forms. You fill them out, provide the docs they require (including stuff like your ID, proof of residence, your fingerprint cards, and that NRA cert showing you completed the class and stuff) You also pay them.

Then, your town has to process your permit application. They'll run background check, log your fingerprints into whatever databases, etc (you'll do this before your application so you include the fingerprints with your app)

Some towns are fantastic and process quickly, some town clerks are major fuckos and purposely try to avoid doing this and delay your app. So you have to stay on top of them.

Once your town finishes your application and you pass your background checks and are approved, your town issues you a "temporary permit". This is *NOT* a pistol permit. This is just a step towards it. Now you have a set amount of days (check for current amount of time, it changed in COVID, I think it's 90 days? maybe less? Don't quote me, do your own research) to take that town's temporary permit to the State Police HQ or one of the satellite offices. HQ is probably the best bet, worked for me. You go there (idk if they do appointments only or walk-ins, call them for that answer) with your docs, and of course that temporary permit. They take your photo, process your information, and complete your permit. You leave with the printed permit in hand.

Once permitted, follow the law. Permits are good for 5 years, and you have to process a new one, similar to getting your Driver's License updated. During those updates, I believe they check your background again, so you better not be naughty.

You pay for NRA safety-course and cert. You pay for fingerprinting. You pay with the town app, you pay with the State PD final application and for your permit. Expect to toss a couple hundred all in.

Oh, also. If you fuck up *ANY* of the forms, they can use that to deny you and there is a probationary period to re-apply. So don't be an idiot. Fill out the forms accurately and follow the instruction of the clerk or the forms themselves. Or you'll be waiting like a year or multiple before applying again. And don't miss that temporary-to-permanent timing deadline, that also automatically disqualifies you. The system is made obtuse and expensive on purpose because this state wants to discourage people exercising that right.