A little late for a reply but you are correct; it is a Softshell Turtle. Now then what species? There is a Smooth and a Spiny.
The one pictured looks like a Spiny: Apalone spiniferous.
I found one of them years ago just across the border in New York State.
You are also correct that they are not known or indigenous to Connecticut but specimens such as your turn up occasionally.
Most probably a release? Thanks for a great picture!