The "other state credit" applies only to income taxed by both states.
If you literally moved from CA to MI (or vice versa), and changed jobs when you did so with no overlap, then you would have no double-taxed income. In that situation you would file two part-year-resident returns.
If that's what happened, check your entries in the My Info section of TT and make sure they are correct. Make sure you allotted your income correctly to each state, and make sure you answered No to the question about Other State Income.
But if you did not move from one state to the other, but instead went to one of the states temporarily for school or work while keeping your main home unchanged, then most likely you would be a non-resident of the "temporary" state while still being a resident of your home state. In that situation you might well have double-taxed income. And you would file one non-resident return and one resident return.
A part-year resident is someone who has literally moved their domicile (their permanent home) from one state to another.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
