Yes, any US Coast Guard Documented vessel that is being used in Connecticut waters for more than 60 days must apply for a certificate of decal. (You must provide valid identification).
All vessels must be registered with the Department of Motor Vehicles (DMV). Evidence of ownership must be submitted at the time of registration. Upon receipt of the application and fee, an identification number will be assigned and a certificate of number/registration will be issued along with two validation decals. The registration will be valid until April 30 of the following year. Connecticut vessel numbers stay with the boat as long as it is registered in the state.
Reference: State of Connecticut Department of Motor Vehicles
https://portal.ct.gov/DMV/Watercraft/Watercraft/Documents-Required-for-Registration-of-a-Boat
