NGP, sorry I was away for the weekend. Hope you've solved this but if not I'll try to help. There's a locked trap door in the floor of an upstairs OFFICE in the Justice Hall. There's 2 "people" in the room. The trapdoor is in the corner, half hidden by a rug. You either need to have a high SNEAK skill to pick the lock or taunt the two witnesses until they attack you before you pick the lock. Once that's done you can go down into the secret library.
There's a librarian who will tell you to leave if you bother talking to her & there's an Ordinator (golden guard) who will say the same. Just don't talk to them & start searching the shelves. The book you need is between the first & second shelves from where you entered. You'll see the Ordinator through the shelf. This means he will also see you. You'll need to use SNEAK again to take the book. When the book is in your inventory, you can walk out the same way you came in without sneaking.