If your permanent home is in Detroit, you are a nonresident of East Lansing. The same rules for domicile apply to your city.
You are a Michigan resident if your domicile is in Michigan. Your domicile is where you have your permanent home. It is the place you plan to return to whenever you go away. You may have several residences, but you can have only one domicile at a time (MCL 206.18). See Form 3799, Statement to Determine State of Domicile.
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