1. No mention of how deep into Connecticut this trip is. The $120 fare is only an estimate made by a poster who knows no more than you nor I, only the OP knows the destination. In any case, you will find espeially in this economy and in non-prime time that reputable trips like this into CN can range from $65 to $500.
2. 20% in NY?? Forgetting something for really really great service or whatever, no New Yorker considers 20% to be standard, that is generally for carpertbaggers. New Yorkers generally double the sales tax and have been doing so for many years, so the average tip is currently slightly less than 17.5% give or tae a slight roundup. OTOH, New Yorkers more than people from other places in the US are apt to more often tip higher for great servce, but ALSO tip miserly for horrible service.
Also New Yorkers are more prone to think responsibly when they tip. What is the difference between a $300 meal for three served with a normal house wine, and a identical meal that costs $3300 because it was served with a bottle of Chateau Lafite? None, and most New Yorkers, will tip on the food amount and a token amount toward the wine (the work performed is EXACTLY the same, and should a restaurant worker make and extra $450-600 commission on your bottle of wine???)
3. Back to the actual subject. The vast majority of Livery Car services in the NYC metropolitan area traditionally do corporate work, and their rates are calculated to include a "tip" for the driver as the average Wall Street guy taking his late night car up to Greenwich for example gives a voucher or uses a code and NEVER EVER tips. Nor do the drivers expect one, as generally they make quite good money.
Most reputable Livery Car Services work on a system where the drivers are owner/operators of their own cars and keep +/- 85% of their receipts, kicking 10% or 15% back to the "fleet" they work with for boking services, etc. Even if the driver does NOT own his own car, he rents it on a shift basis, these guys do NOT work for a "wage" and other than their "rent" and gas costs pocket everything they make. Incidentally ALL NYC yellow cabs also work under the same principle. Depending on car/driver/deal/shift a 12 hour shift costs anywhere from $50-100 for Yellow Cabs per 12 hour shift. I do not now what it currently is for non-Medallion cars, but I would imagine that it would be similar.)
4. In short I would say that $5-10 would be okay, $20 ridiculous.