Self-employment tax is not paid to any state, that is your FICA (Social Security) tax.
If your schedule C income was earned in Michigan, you would need to claim that gain on a non-resident Michigan tax return.
You would need to allocate the income by using a logical formula of the time in the state, and the profit earned on that revenue.
Keep a record with your tax files of how you determined the income you allocated to Michigan.
Any Schedule C income from a Michigan source while NOT physically in the state of Michigan would not be claimed.
Any Michigan tax due may be a credit claim-able on your resident state return, depending on that state.
Michigan Income
"You must file a Michigan Individual Income Tax return and pay tax on salary, wages and other employee compensation for work performed in Michigan."
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