To own an SBR in Michigan is the same as to own in anywhere. You do have to follow all federal laws.
To build or buy an SBR you must register it with the ATF per the National Firearms Act. (NFA)
As an individual you must
Fill out a form 1 (build) or form 4 (buy), have your sheriff or chief LEO sign it. Then have your fingerprints taken. Send in the completed form, your fingerprints, a check for $200 dollars, and wait about 5-7 months right now, and once approved you may take home or build your SBR.
If your sheriff won't sign or prefer to have the benefits of a trust.
Go to a lawyer or use a service to create a trust for that trust to own the gun. Go have it notarized. Fill out a form 4 to buy or form 1 to build a SBR, pay $200 tax stamp, wait 5-7 months.
With both options if you choose to build and not buy a factory SBR you must engrave the firearms with your name and city and state. If its a trust you engrave the trust name, city and state.
Check the class 3 section in the armory section of the site.