I suggest that you go to the website of both Michigan and North Carolina to check that out. I have seen a number of vessels in NC that were ASME Code stamped but not registered with the National Board.
You must register to download some documents, but there is no charge to do so. One other easy way is to go to their website and click on Jurisdictions/our members and go the the state or Canadian province in question. There you will find links to the actual state websites plus a quick overview.
I registered and downloaded the synopsis. It was very easy and only took a few hours for my registration to clear. There is a very helpful chart showing which states require NBR. Michigan is not one of them. North Carolina is.