Michigan and Ohio have a reciprocal agreement, also called reciprocity, which is an agreement between two states that allows residents of one state to request exemption from tax withholding in the other (reciprocal) state.
If your employer has withheld taxes for the work state, you will have to file for a refund from your work state. You'll still file your resident return that also includes that income and pay tax on it. You will file a Ohio return to get the money withheld.
You can file an exemption form to not have withholding from that state, be sure to ask your employer to withhold taxes from your resident state.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"