You would have to be an expert level swimmer, and have a chase boat with a well trained rescue swimmer/ take all waranted precautions, but im sure it's been done countless times over the years. But, that river has taken many lives. Is this more of a hypothetical question or do you plan to do it once its warmer?

Legally, I haven't heard anything that would stop you and it would be really hard for anyone to try considering the countless places that you can enter it. But there is a law for everything, it seems, so I wouldn't doubt something being in place.

Someone swam across the Atlantic so the CT River is not all that nuts.