Snowmobiles that are ridden on public land must be registered with the state. You can register you snowmobile at your local DMV. Snowmobiles used on private land do not need to be registered. Out-of-state snowmobiles can be registered in Connecticut by presenting an out-of-state registration, out-of-state operator license, Application for Registration and Certificate of Title, and a $35 fee.
Check out these Watertown, CT ATV/OHV resources: