State tax filing

Can you help with Michigan tax withholdings, I work in Michigan, but my address is in Ohio, I have 9 months of withholding in MI, and asked my employer to change to ohio after I found out. 

Since MI and OH are reciprocal state, one who lives in one state and work in another can only pay to one state. 

and I am full year resident to OH, so I think of my action would be : 

1 file for full refund for MI withholdings 

2 pay for OH tax 

Can you tell how should I do it ? 

Many thanks