You appear to be referring to supplemental property taxes that might be eligible for a property tax credit on your Connecticut return, as opposed to the vehicle registration deduction allowable on your federal return.
If that's the case, then, according to Which Property Tax Bills Qualify under Schedule 3 – Property Tax Credit in the Connecticut Resident Income Tax Return Instructions, "[s]upplemental property tax bills that were due during 2023 or 2024 … qualify if paid during 2023."
This language doesn't speak directly to when the taxes were assessed, but, logically, if they were assessed in 2021 or another prior year, they'd still be due during 2023 or 2024, and should qualify if you paid them in 2023.
If you're referring to the federal itemized deduction for vehicle registration fees, auto registration fees aren’t deductible for Connecticut, but you can claim the personal property tax you paid annually, based on the value of your car. See the TurboTax Help article Is my car registration fee deductible? for more information.
