choshen mishpat civil law - Are parents responsible if their children damage in a store?

If a parent brings a child (defined as under 13 for a boy and under 12 for a girl) into a store, and that child damages an item, is the parent responsible to pay?

Would it matter if the child simply damaged an item (e.g. pushed a crystal vase, and it shattered into ∞ pieces), or if the child actually benefited from the damaged item (e.g. consuming a candy)?

(answers should focus on the Jewish law aspect and ignore issues of civil law)