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You are correct, no inheritance tax in Michigan (presuming the decedent resided in Michigan). There is no federal inheritance tax either.
There is estate tax, but presumably if there was estate tax (either federal or state) it will be paid from estate funds before distribution to beneficiaries.
You do not include inherited funds on your tax return---with the exception of:
1. Any interest, dividends, or sales of property made after the property/funds became yours.
2. If any of the inheritance is from tax-deferred funds, such as IRA, 401k, pension, etc. In this case, the funds would be taxable to the beneficiary in the same manner as they would have been to the decedent.
If you need clarification, let me know.