Connecticut will probably become Republican or swing in the future, but 2016 is too early. I see a definite trend though. I hope its plausible in 2016, but seriously doubt it. Its only plausible in an Indiana 2008 scenario, where the GOP massively spends and visits while the Democrats don't take it seriously enough.
Absolutely no reason that this would be the case. Wealthy white suburbans are not becoming more Republican (and especially not so in New England) and the Hispanic population in Connecticut is only increasing.
Between the increasingly liberal New England suburban demographic and an increasingly diverse state, Connecticut is instead a prime target to become even more solidly Democratic.