Cats are legally classed as a "free sprit" or somesuch and you cannot be held responsible for damage they cause, unlike a dog where you are responsible.
From a purely legal point of view i think you would not be liable, the person who brought the animal to the vets would be liable.
I cant remember the exact working but dogs and cats are treated very differently in the eyes of the law. If your dog bit someone on the street you would be legally responsible, but if your cat bit or scratched someone you wouldnt ( something to that effect anyway ). Legally you dont "own" a cat in the same sense that you own a dog.
Morally of course its your bill to pay.