We don't know if we paid the tax back then or not, or whether or not any filing was made. Still researching this, but haven't found the sacred paper. I've read the law (Michigan Senate bill 337 sec 27a(2), amended in 2014, but it is not very clear. It says
"A deficiency, interest, or penalty shall not be assessed after the expiration of 4 years after the date set for the filing of the required return or after the return was filed, whichever is later..."
I think they interpret it to their favor --i.e. if no return was filed they say the limitation never starts. I would say it was intended to allow auditing time for late filers that might put in an amended return for a refund. But in practice, it appears that as Marc said, if no filing was made, then there is no statute of limitations. If that is the case, then they can audit and assess the tax if they choose to do so as a matter of policy within a prescribed time from discovery. Problem is, if I get the lawyers and CPAs involved at $200+ per hour each, then we might as well just turn over the airplane anyway.
The takeaway of this post is -- Don't make assumptions about state "use" tax, make required filings, keep records forever, and check before you move an airplane to another state.