Check with the car dealer that you may buy from and ask him if Connecticut allows for a no sales tax transfer out of state. Missouri and many other states allow this kind of transfer, knowing the item does not stay in state for taxation purposes. You then pay sales tax on the vehicle in the state where you are licensing it. Kansas collects sales tax at the dealer on the bill of sale, and does not allow for such a transfer, but Missouri allows credit for any sales taxes paid to Kansas. Private sales also follow different rules in KS.
As you can see, you need to ask the right questions from either the DMVs involved or the dealer involved.