Most of the Connecticut River between Canaan and Colebrool, and south of Bloomfield, VT, has enough water to paddle all season.
Upstream of Pittsburg, look for 500-1000 cfs on the Pittsburg Gauge. Between Colebrook and North Stratford, you may hit bottom with a loaded boat in a few places when there is less than 500 cfs on the North Stratford Gauge.
Use these gauge heights to make informed decisions regarding whether conditions are too high, or if there is adequate water to paddle the upper most reaches. There are a couple places to check current water levels:
The National Weather Service's Advanced Hydrologic Prediction Service CT River Predictions Center which indicates flood levels and predictions for the next few days,
Finally, Great River Hydro provides flow forecasts for areas below their dams at: