Non-Resident and Resident for the same state?

So I have a very weird situation. I got transferred from Texas to Michigan for my company, but started working and getting paid by Michigan payroll two months before I could move there while working remotely. So as of such I was paying Michigan state/local income taxes on my payroll (work wasn't set up to do anything else) while I was a non-resident. This is especially annoying because Texas has no state/local income tax.

 

I ended the year a resident in Michigan. 

 

Can I file both a non-resident and a resident state return in the same state for different periods of time? If not, how do I reclaim this mis-taxed income?

 

Thanks!