The following assumes your spouse is a civilian.
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...Well, that can get a bit touchy.
Normally, you have ~90-to-120(??) days after leaving service to re-establish your residence in your HOR (or State of legal residence if you changed your SLR state with a DD2058 it sometime during your service service).
Many times, though, separating service members just remain in the state where they are actually living when they retire. When that happens, they are considered residents of the state they are in, as-of the separation date on the service person's DD214.
Now, if you are receiving some post-retirement training (non-military correct?) in another state after retirement, and are not actually moving your residence to that state...then you are receiving $$ there as a non-resident (and subject to non-resident income taxes in that state...if that training state has an income tax). And if your home where your spouse still lives is in another state, where you intend to return, then that spouse's state will be your state of residence....since you are no longer in the military, and don't get to keep your Military state-lock.
That's my considered, non-legal reasoning.
...but like I said, it might get touchy....like terminal leave before retirement...starting that (civilian?) training before you "Officially " are terminated from service?
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
