Hi,
Firstly, if the person is even remotely popular, be prepared to queue for at least 3-4 hours before the signing! You'll be surprised how many people turn-up at these things!
Technically, you should buy the book from the store that is doing the signing. However, not all stores enforce this rule, nor necessarily will the people who are doing the signing (or their managers/bouncers/PA).
If you don't want the book, in question, because you can get it cheaper elsewhere, or already have it, it shouldn't be too wildly inappropriate to bring another item to be signed instead (or to sneak in your copy, you've already bought).
However, once again, it does depend on the store, the person doing the signing session, and whether you can just turn-up on the day in question and queue to see your chosen personality, or if you have to buy tickets to it.
If you have to buy a ticket for the signing, unless it stipulates on the Terms & Conditions on it, that only items purchased at the store can/will be signed, then you should really be allowed to take something of your own to be autographed.
But, having said that, if it's a freebie signing, and the personality is popular, time and the store itself may dictate what the celebrity will or will not autograph. Some stores and celebs will sign anything and everything you ask, others will restrict you to only merchandise bought at the time, and others will restrict you to just one item, but
any single item, bought on the day or not.
If you really want their autograph, why not take along your copy, buy another one, get both signed, and then flog the unwanted, autographed one for a reasonable wad of cash?!
That's a nice way around the situation!
Pooch