Your severance would be taxable in the same proportion as the rest of your work.
Michigan says:
Vacation, holiday, sick, severance and bonus pay to nonresidents who perform part but not all of their work or services in the City of Detroit are taxable in the same ration as their normal activities.
Example: A nonresident employee who is subject to withholding on 60% of their earnings, because 60% of their work is performed in the City of Detroit, is also subject to withholding on 60% of their vacation, holiday, sick pay, severance pay, bonus pay or wage payments during periods of sickness.
See What type of compensation do I have to withhold from?
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