It looks like the course is 8 hours not 5.. but, it looks like you can pay a fee ($75.00) and take an equivalency exam, and skip the course.
Maybe that's what ASA ( school? ) is refering to? Can't say.
DEEP: Certification Requirements
See also the FAQ.
Unless one of the ASA instructors is also a proctor for the state, it looks like you might have to take another exam.
But, no...I have no specific knowledge of Connecticut laws, other than what I just read.
There's a few NJ schools that offer a combo ASA cert and a Boater Safety Card..but generally speaking they are two totally seperate courses.
i.e. ASA doesn't cover trailoring, jet ski's etc etc.