I am in the military and a resident of Michigan. Military pay is 100% tax free in Michigan but on the tax return it shows I owe money. How do I fix this?

Double-check some entries in TurboTax.  On the Personal Information screen, make sure that you have marked that your state of residence is Michigan, and that your state of work is Michigan.  Make sure that you have selected that you are active-duty military, and that your W-2 is Active Duty income.  This option is available on the first screen after entering in all of your W2 information.  If you take all of these steps, the Michigan tax should zero out.  If it does not, then carefully navigate through the Michigan screens, and you should see a selection to include that income as active duty income.  

But once it is coded correctly, the income will be deducted and not taxed in Michigan.