If you live and work in CT, then you should be filing a CT state tax return. Your CT address is the one that should be on your tax return so that the IRS and state know where to send you a letter or a check.
As for the driver's license......if you live in CT you had 90 days to get a CT license---so you should take care of that.
https://portal.ct.gov/dmv/licenses-permits-ids/transfer-out-of-state-license?language=en_US
But did you move during 2023? Did you live and work in NY for any part of 2023?
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