OK, I will sum up from this discussion what I think I understand to be the law. Feedback would be appreciated:

1. Some larger Connecticut waterways such as the Farmington River in Farmington are public waterways in that both the water and the stream-bed are in the public domain, private property lines are fixed, ending more or less around the spring high water mark. Looking at the Shetucket River flowing through Sprague, it appears from town zoning map that the stream-bed is not privately held. In such waterways it would not only be permissible to float the river so long as there are points of legal access, but it would also be legal to stop, anchor, or wade in the water over the public stream-bed. Also, in times of lower water, areas above water within the stream-bed would be legally accessible. It would only be not permissible to cross fixed property lines onto private property along the banks without permission unless under water in spring flood, then point 2 would then apply. However, government entities could put additional restrictions on such public waterways.

2. In Connecticut where public water flow passes over privately held stream-bed land or is a lake/pond over private land, it would be legally permissible to float this waterway if public access is available or if one of the private landowners grants permission to access. It would not be permissible to touch the bottom with foot or paddle or anything of substance besides water without landowner permission. This would include landowner structures such as a fence across the watercourse. I believe that would mean ice fishing or walking on the ice would be legal under the same definition, but it would be illegal to sound the bottom through the ice with a sinker. With reference to macattack678's post, the land under Pendleton Hill Brook and Spalding Pond shows from North Stonington GIS records as entirely private, shared by a few property owners. He would need the permission of one landowner to access the entire pond. The small stream might be very difficult to navigate from the public road bridge. I could not see the stream from aerial maps.

3. Where there is not clear regulations in state law on a given murky issue, the definition of permissible activity may rest on prior precedent Connecticut settled riparian case law.

4. Most any waterway worth rafting/kayaking in Connecticut can be researched for the legal status with regard to points 1, 2, and 3. I imagine such research has been done already by groups like ctwatertrails.org, and it would be neat if this information could be located somewhere online.