I filed my state return, and received a small refund, but now the state of michigan is telling me I owe them money with no explanation? How can I find out why?

Call them and ask if the notice is not clear on what income was not reported on the MI return that was on the federal return. Only they can explain their own notice. 

Before calling, look more closely at the notice. There's usually an attachment that shows line by line what was changed.

"based on information from the IRS regarding adjustments/unreported income"  usually means you failed to report a tax document that the IRS received.  Common omissions are form 1099-B (stock and mutual fund sales) or 1099-Misc (side gig income)

Unless you can show the IRS that they made an error, you're not going to beat this one, so just pay it.