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.
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.
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.