There are paramedic training programs all over the state of Connecticut which specialize in teaching how to treat injuries or other medical emergencies for transport and stabilization to more central care centers. These training courses are regulated by the Connecticut Office of Emergency Medical Services (OEMS), who is also in charge of all emergency medical technicians and paramedics. EMTs and Paramedics across the state are comprised of a number of paid and volunteer positions.
In order to become a paramedic in Connecticut, one must be a certified EMT, having passed the NREMT - national registry of emergency medical technician - exam, and also advance through a practical test in order to demonstrate your field skills in recussitation and preparedness.
The CT OEMS page is located at http://www.ct.gov/dph/cwp/view.asp?a=3127&q=387362