No. Even though IN had your money, you were late with the Michigan payment.
Since Michigan and Indiana are reciprocal states, you need to complete form WH-47 and give it to your employer so he will stop withholding INDIANA TAX. He may be able to withhold MI tax instead. If not, you should send in quarterly estimated payments.
If you paid IN county income tax, in addition to state, you cannot get that refunded but MI will give you credit for that on the MI return
