Well, that's the question, isn't it? Does Michigan have an open primary or not? Are the only people who can vote in a party's primary those who actually "belong", i.e. pay dues and have a membership card? Or do they just declare on election day or when they register? How is that determined under state law? I don't know and, unfortunately, this article doesn't seem to cite any statute or provide an answer.
I live in Michigan, and I don’t think you have to be a member of any party to vote in the primaries, you just have to be registered to vote.