I moved from Colorado to Michigan in 2021. I contacted the pension fund management company and changed my address in November 2021 to Michigan, to be effective 1-1-2022. They screwed it up and withheld Fed & State tax for Colorado for 3 months until I caught their error. I called them to get a re-issued W-2 and they told me it couldn't be done even though it was their mistake. I don't know how/what I'm supposed to file to get a refund for the Colorado state tax withheld.
You just need to file a CO non-resident return with the information from your W-2 to get the refund. When you are entering your 2022 tax return, be sure to list the CO withholding as a separate state on the W-2 and keep your returns marked that you only lived and worked in MI for the whole year. TurboTax will prompt you to complete the CO non-resident return if you want to.
If you do not want to use TurboTax to file the form, you can see CO Non-resident Return to download the forms and instructions to complete a paper return yourself.