We don't know what the limit is for sure because we don't hunt anywhere near any residences.
Assuming it's legal to shoot where you are, (we live in the city-not allowed at all here.) you can find the distance limit by checking the DNR website. Look for the hunting guide and check the firearms section where they list what kinds of gun you can use, shotgun zone, etc.
Remember, in Michigan, if you have a CPL, you can carry while hunting, even during archery season, but it must be CONCEALED.