CT is a little different than most states as it has a couple of ambulance services that use high school students as volunteers to staff their ambulances. There was recently a thread on Darien Ambulance not too long ago which showed the teenagers as the driver of the ambulance as well as the EMT taking care of the patient. What the ambulance service may save in salaries, they probably pay out in insurance.
I'm a volunteer firefighter in Connecticut, currently waiting on my results from my EMT-B exam. If you're under 18 years old you can get your Connecticut EMT cert, but you will not be able to apply for the national registry until you are 18.
As aforementioned, you may not be able to do much with it because of insurance issues. However, it's a great way to clock a year or two of experience if you get your certification and run on a volunteer crew. That is, if you have intentions of making a career out of it in the future.