You only need to file a Michigan state extension if you expect to owe taxes to the state of Michigan. If you'll be getting a refund, you don't need to file a Michigan extension.
If you will owe taxes and want to request more time to file your Michigan tax return, send a payment of your remaining estimated tax to the Michigan Department of Treasury with a copy of your approved federal extension (U.S. Form 4868) on or before the original due date of your return. The Michigan Department of Treasury will extend the due date to your new federal due date.
If you don't have a federal extension, file an Application for Extension of Time to File Michigan Tax Returns (Form 4 ) with your payment. The Michigan Department of Treasury will not notify you of approval.
Detroit Returns: Detroit extensions are not required if you're expecting a Detroit refund. If you need to file a Detroit extension, file an Application for Extension of Time to File Michigan City Tax Returns (Form 5209 ) and submit it to the Michigan Department of Treasury with your city tax payment.
Other Michigan Cities: If you need to file any other Michigan city extension, you'll need to fill out a form from your city's website and submit it to the city with your city tax payment.