You should never have to pay 2 state taxes on the same income. Or to be more precise you get a credit on taxes you pay to other states on your state of residency. So effectively you never pay more than 1 state. If for whatever reason you end up in a situation like this you will effectively pay whichever state has the highest tax but not both. You could still pay NYC tax though on top of CT I think if you had a home on both places and spent any part of a day for more than 183 days in NYC I think. Though the tax should still be a credit against CT if CT is your permanent home.

Edit: Wow after some research having a place in NYC that is not your permanent residence no matter how many days you spend in NYC does not get you taxed as a NYC resident anymore. This was changed 4 months ago.

https://www.troutman.com/insights/ny-supreme-court-rules-taxpayers-ny-vacation-home-not-permanent-place-of-abode.html