There is no requirement to inform the officer you have a firearm during a traffic stop.
There is a case out of Virginia I just saw that is very similar in nature to this:
And of course the always present Terry v Ohio:
The police would argue that you were frisked for 'officer safety', but this is unreasonable since they knew you had a permit and had no reason to suspect you were dangerous. A permit is not RAS for a crime, since anything they could possibly turn up would not be a crime based on the simple fact that the permit was present.
I would immediately file a complaint with the Naugatuck PD. I would also immediately send out letters for FOIA requests into all radio traffic and communications about your stop for that night. You should probably also seek the counsel of Attorney Rachel Baird. She will know how to handle this.
Your rights were violated here without a doubt. The police were either misinformed or they were malicious, and they used it to violate your 4th amendment rights.