The idea is that until a contribution is legally accepted as a contribution to an HSA or an IRA, it is tied to a certain year (and month, in the case where you have changed states).
Once the contribution is accepted under the rules, it just becomes part of the giant pot of money in the account. It loses its identity and history - it does not matter what year or state the contribution distributed (assuming that you could isolate it anyway) was made.
If I understand your question about the 1099-SA taxable distribution, the short answer is "no" because TurboTax has no way of knowing to which state it belongs. And I think (without giving it a great deal of thought) that the 1099-SA taxable distribution would be reported on the NY return, and then a credit for the taxes paid in NY would be carried over to CT, so, in effect, CT would not get the tax, even though the income appears to be reported.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"
