No, Form 1040 does not get filed with your Michigan state return. If you are not e-filing your federal return, you will need to file Form 1040 with the IRS.
If you file certain Federal schedules or forms with your federal return you must include a copy with your Michigan income tax return. To see what federal schedules you file with your Michigan return go to see Table 3, page 59 here: https://goo.gl/GJV7zH