From the CT boating guide.

To legally operate any boat with an engine or motor, other than
a personal watercraft, or a sailboat 191⁄2 feet in length or longer,
the following persons must obtain a Safe Boating Certificate or a
Certificate of Personal Watercraft Operation:
• Residents of Connecticut
• Owners of real property in Connecticut
• Anyone using Connecticut waters more than 60 days in a year.
A person who has a valid vessel operator license by the United States
Coast Guard does not require a Safe Boating Certificate. They must have
a copy of the license on board the recreational vessel on which they are
operating.
To legally operate of a personal watercraft, regardless of state
residency, you must possess a Certificate of Personal Watercraft
Operation to operate on Connecticut waters.
The Connecticut Safe Boating Certificate and Certificate of Personal
Watercraft Operation are accepted in many states. Connecticut
recognizes certificates from New York, Massachusetts and Rhode Island
for use upon our waters (see page 12, Reciprocity).