First, of course, chances are your book will have to be in hard cover, or libraries aren't likely to take it. At the very least, it has to be in trade paperback. Ordinary paperbacks have a very, very small footprint in most libraries.
Your local library should carry your book because they
know you. If you aren't a regular patron, why would they care about a phone call?
If they do know you, it's a good idea to donate a copy or two. This won't harm your sales, will probably help them, and donating to a cash-strapped library means they'll be grateful.
And for the most part, libraries do not get their books from publisher contact, though many libraries do receive various catalogues from publishers, at least the ones in my state. Libraries in my state, at least, choose their books from two primary sources. One is the bestseller list, and the other is from reviews in such places as Library Journal.
http://lj.libraryjournal.com/
But for local libraries, get out and do your own contacting. It's silly to hope the publisher will do it, or that your book will automatically get a review in Library Journal. Go to the local libraries in person and talk to them. If need be, donate books to any nearby library who will take them. Most libraries love local writers, and want their books on the shelves, but they have to k
now you.
And whether they buy it, or you donate it, you really want your books there. The more library patrons who read your book there, and like it, the better. Libraries are still where many readers find new writers, and if they like the first book they read, they'll start buying other you write, and even the one they read free from the library.
Libraries are always cash-strapped, they can only acquire so many new books each month, and unless you're a famous writer, you won't be on the automatic buy list.
But wherever you are, you want to access local libraries personally. Shelf space is scarce world-wide, libraries can only take a tiny fraction of the books published each year, and I mean a
tiny fraction. You have to give local libraries a reason to choose your book over the thousands of others wanting the same shelf space, and the only way to ensure this is to be a regular visitor to local branches. If you're friends with libraries, libraries will be friends with you. Expecting anyone else to get the job done, your publisher, or reviews, etc., just won't cut it unless your book is a bestseller.