A great place to start is the State of Michigan's Film Michigan's website at: http://www.michigan.gov/filmoffice (or see link below, under Resources). On this site, you will actually find the list of upcoming movies that are coming to Michigan and a job listing area, too.
Another great link on the Film Michigan site to check is "Films Coming Soon to Michigan." This page will show you the movies that are coming to Michigan to film. You can then google the name of those movies to see if you can find out more information on when the film is coming to shoot and what town it will be shooting in. They may even have information on their websites on how to become an extra in their movies.
Still another way to find out how to become an extra in a Michigan movie, is to watch your local news and read your local newspapers. You can even set up a Google Search that will notify you of this information, by setting up a Google Alert with specific keywords. Some good keywords to use would be: Michigan Movie Extra Filming , etc.
Another great website to check is Michigan Film. (See link below). They have job opportunities listed for upcoming movies, and the city that the movie will be filmed in.
I hope this information was helpful to you to start your research on how to become an extra in a movie in Michigan...now, go break a leg!