Minnesota is one of just 7 states without a state fossil. The Science Museum of Minnesota has a page up with 8 possible candidates. They include a saber-toothed cat (Homotherium), a trilobite (Dikelocephalus minnesotensis), a large shelled cephalopod (Endoceras), and some large mammals (Bison antiquus and Mammuthus columbi). There's even a shark (Squalicorax)!
Here is the form to vote. So, hurry on over and check out the list!