The Osterlin Library has just a few books with collections of written music. Browse the shelves from M1 to M5000 to see what's available.
The public library has a larger collection of popular music books. Visit Traverse Area District Library and browse the shelves in the 780 range to see what they have.
Public domain sheet music is widely available online. Check out the sites listed below to get started!
The International Music Score Library Project, or Petrucci Music Library, "is the largest collection of free and freely available recordings and scores on the Internet" (Choice Reviews). Start searching here.