I'm in the process of getting one now. All you need is a letter from your doctor saying you qualify for the handicapped licence per section 26-29b which, as O-bass said, says "Any resident with the loss of a limb or the loss of the use of a limb and a doctor’s certificate may be issued a free license. Qualified nonresidents who are residents of states which allow CT residents the same privileges are also eligible".

The first letter my doctor wrote was a little vague so I was turned down 3 days after sending it in. The second letter he wrote left no doubt that I qualify for the handicapped licence. It's now been over 2 weeks since I submitted it and haven't heard anything.