Registering a car as classic

Does anyone know what I need to do to register my car as a classic in Connecticut? I have a 2004 BMW 330i whose registration I renewed this year (actually it lapsed in 2022 so I had to pay a fine, oops). I don't actually drive the car very much so I was thinking it might be a good idea to register it as a classic to save on insurance and taxes.

I asked the person at the DMV what I need to do to register my car as a classic and they said it's not eligible for that for another 3 years, which seemed weird, but I didn't argue. But something about that didn't seem right to me so I checked and the threshold is indeed 20 years, which means my car should be eligible.

Unfortunately, I cannot find anything on the DMV website about this, what I need to do to register a car as classic, or what that will mean for me in practice. Can anyone point me to any resources about this?