Moved to a state without income tax without telling my employer

i have a hypothetical scenario. let's say i don't tell my current employer in michigan that i have moved to texas and they withhold my state taxes for the whole of 2021 and report my income to Michigan state. Then in 2022 when i file my taxes, Will i able get my taxes (refund) back from michigan state when i file non-resident michigan state taxes that my michigan employer withheld ?