My own local public library hasn't accepted my book, yet, though it was donated, apparently on the theory that I'm a local but not really an "author" (PublishAmerica appears often to be thought illegitimate). But the University of Kansas shelved it very quickly, as did the Luther Seminary library in St. Paul, MN and the Gordon-Conwell Theological Seminary. (Yes, my book pertains to Christian theology).
Libraries are a great way to meet people. Usually the PR person is pleased to have people volunteer (especially local authors) to do a Book Reading or Poetry Reading event or give a talk on your book. I have found libraries a great way to promote my books and newspaper column. What does local mean? To me, it can be a 300 mile radius / local = statewide. Why not? Hope this is helpful.