Not in Connecticut, but there is very little gold, I believe that in New Hampshire, Vermont and Maine, there are a lot of gold to find. No permits are needed in these states. Good hunting and good luck.
Post your question in the gold prospecting section so the proper people will see it. I know we have miners from Oregon who can answer your question with current rules for where you actually asked about.
No you do not. You can sluice also no permit needed. No pumps...gas or electric on the beach. You can incorporate a pump above the vegetation line. (Highbanker, Gold Cube etc.)