This is a common occurrence, I know people who moved and then only remember the next spring during tax season that they never filed a new state version of a W-4. Which means for 3 or 4 months in the new year money is sent to the wrong state capital, and way too much was sent the previous year.
In the spring of 2016 you should have filed a non-resident tax form with Michigan. On that form you would specify your total income numbers, your Michigan income numbers, and your other-state income numbers; with Michigan + other equal to total. That should have resulted in getting all the state taxes that were sent to Michigan returned.
It is possible that the online software is unable to complete the non-resident tax form. Not all forms and situations can be addressed by the software. So you may need to fill out paper forms.
You should be able to find what you need on the state of Michigan website for 2015 Taxes.
A quick read shows that you will probably need the Michigan 1040, schedule 1 and Schedule NR
You may run into an issue if your license, car registration, voter registration, and other documentation point to you being a resident for the part of the year you earned that income. That means you will have to submit Form 3799 Statement to Determine State of Domicile
You want to do this soon because there are deadlines that limit how far back you can files taxes. The state may also get tax information from the IRS and could decide that all your income from 2015 should have applied to them, so they will be sending you a tax bill plus penalties for failure to file.