There are quite a few Native American tribes in that area. To name a few Fox, Sac, Ho-chunk, Santee Sioux, Northern Chippewa, Both Sub-arctic Cree and Plains Cree not to mention Odawa, Illinois, Miami, and a whole slew of others. Some of the tribes were horse culture and some were not. Other than the Miami I believe you will find the bows were the regular square section hardwood self bows because that geographic area is still in the abundantly wooded area. I believe you will find that a lot of the bows were either Ash, Ironwood, Hickory, or osage....some of the northern tribes would have also used birch. I have only seen one example of a sinew lined bow from the area and that was northern Cree ( plain wood, sinewed lined and decorated with deer foot prints in black. Carved edge bows were quite common amoungst the Fox, Sac, Ho-Chunk and of course thw Chippewa and Odawa. For the most part the bows will be a square sectioned, hardwood, between 36" and (about)54, no grip wrap and either single curved or slightly double curved.
If have a particular tribe in mind I can see if I have photos of any of the appropriate bows squirrled away.
rich