While I like the idea of cats in libraries (I like cats, I like libraries, why shouldn't they go together?), I always wonder about the wisdom of such a decision. Cat allergies are very common.
Perhaps one cat in a large library doesn't have much of an impact on allergies, but watch out for the cat's favorite chair or shelf of books. I know my cat finds it rather entertaining to climb on top of the books on one of the bottom rows of my book shelves.
For a map of libraries with cats (both alive and statue/stuffed animal), check out Iron Frog Productions' Library Cat Map.