I am not familiar with the law in regards to OC in metro parks (state controlled)? I am sure many here are and will be along shortly may I suggest you invest a few bucks ($10 to $15 buys a copy of this very detailed OC book PDF download version is the cheapest) it covers just about everything imaginable when it comes to OC in MI.
Link -->
http://www.citizensleaguesd.com/p/store.html
Chapter 9
STATE PARKS, STATE LAND, NATIONAL PARKS AND NATIONAL FORESTS
If no one answers I suggest you PM Michigander (tell him G9OS sent you) he wrote it and he should be able to give you a answer on this. sadly, I have not been to a state park in years but it is still good to know the answer in case I may want to go to one in the future.
Bests of luck in your OC adventures
G9OS
It's actually The Huron-Clinton Metropolitan Authority and it is not part of the state park system, it's an "authority"... you know, much like CDL is an "authority". Now perhaps some will see why the library issue in Lansing will have huge repercussions.
Here's their rule on firearms:
FIREARMS AND OTHER WEAPONS- No person shall possess or control any rifle, shotgun or other firearm, bow and arrow, slingshot, pellet gun, air rifle, fireworks, explosives, or other dangerous substances within the boundaries of any park, without written permission of the Authority; provided, that this rule shall not apply to any law enforcement officer who has been duly appointed by the government of the United States, the State of Michigan or any county, municipality other political subdivision of the State of Michigan;
and provided, further that this section shall not prohibit a person from legally carrying firearms in accordance with state law, including transporting an unloaded shotgun in a case within the boundaries of Lake Erie or Metro Beach Metropark for the purpose of using Lake Erie or Metro Beach Metropark as access to a permitted hunting area.
see
http://www.metroparks.com/content.aspx?ID=127
So it appears as long as you are legal under state law, you should be fine. But then again, in light of CDL's Library rules which also mention state law... I would be careful here.