Seems a little over the top. Just charge her for what the book is worth, and end it there. Shouldn't even involve the cops, this should have been settled by the library directly. An easy way to do it would be to just require a deposit each time you borrow a book. You get it back when you return the book, if it's late, you get a partial.
Reminds me of a story about someone being arrested for a late blockbuster VHS tape like maybe 10ish years ago. That blockbuster had been closed for like a decade. It's ridiculous that cops spend their time chasing dumb cases like this instead of stopping theft, drug trafficking, human trafficking etc. It's not so much individual cops fault but just the system overall that tells them what to focus on. These days they seem to just turn a blind eye to actual real crime that affects people and focus on the petty victimless crimes.