Yes, it's possible. The train from waterbury to Bridgeport (where you can catch a train to New York) runs twice a day. Its leaves waterbury to Bridgeport between 11am and 12pm and also at 4pm. Be sure to give yourself some range because sometimes there are delays and/or early departures. To my best of knowledge!
Waterbury train takes u into Bridgeport. Where u can transfer there for train into Grand Central. But then you need another train to take u to Port Authority. Better way i think is to take Amtrak out of New Haven to straight run into Port Authority.
Yes I believe you can pick it up in Naugatuckthere you can catch the train to Bridgeport and I believe they're you pick up another train directly to Port authority
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