Because Michigan and Ohio have state tax reciprocity, you should be receiving a refund for the taxes paid to Michigan.
Make sure you are reporting your residency as you home in Ohio.
She may owe city taxes which are not covered by the reciprocity agreement, but she doesn't owe state taxes to MI.
You need to complete the Michigan Non-Resident Income Tax return before the Ohio Resident Income Tax return to ensure you receive credit for the taxes paid to the other state.
For more information, follow this link:
https://www.michigan.gov/taxes/0,4676,7-238-75545_43715-154059--,00.html
