I was just looking around the MI SOS (Secretary of State our MI DMV) web site.
Only because what you have described isn’t what I have done in the past for out of state purchases as a MI resident. From what I read MI may have negotiated reciprocating agreements that may differ from state to state. This http://www.michigan.gov/documents/485_72279_7.pdf looks like the form for MI dealers use to compute and collect taxes for out of state residence purchases. I will admid I didn’t read it completely it does kind of eluded to something a little different for each state.
Like someone else said MI has been changing some of tax laws. Just in the last couple months MI changed the law for a trade in, that trade value is now exempt from sales tax. The dealers have been lobbying hard for that for a while now. Like someone else said you really should call a SOS branch office to make sure you are armed with the correct info.
Sorry not sure how you put a hyper link in this site I tried HTML code and it didn't seem to work??