I did that just recently. It depends on the book store. You might call the store first to see if they will allow it.
I think if you explain you are a blogger, it might be different. Smaller book stores, authors and publishers love it when you post about the signings. I have even posted notes about tours on my blog. B&N won't let you take pictures, but I have done it sneakily!
I had authors sign my ARCs at a book fair and then I gave them away on my blog. They were really happy about that!
The signing is at the library...would that be okay? or would I have to call or something?...
I was debating like is it or is it not okay, since the book is out...were you able to get yours signed??
I think it's fine! Authors like fans, and they will figure that if you have an ARC you have some amount of influence (which is true!).
I have taken ARCs to booksignings and it's fun; it can be a little conversation starter. In one particular case, I have spent at least $100 over the years on this author's books and done a half-dozen glowing reviews because I LOVE her work, so no, I don't feel guilty about not spending money at that particular moment in time. People often bring in dog-eared backlisted favorites, too.
Some bookstores do have policies about bringing in books purchased elsewhere but I wouldn't worry about it at all at a library.