I grew up in Michigan and attended UM. I can say anecdotally that very, very few people I knew (mostly from math + engineering) stayed in Michigan after graduating. On the other hand, many people I knew who graduated from Michigan State ended up taking jobs in and around Detroit.
I found an article [1] which claims that 40% of UM's living alumni currently live in Michigan. I would wager that the rates for recent graduates are even lower, since moving away from family has become more common, but I couldn't find data.