The legal systems in most states -- whether by statute or through court decisions -- recognize that parents have a legal duty to take reasonable steps to supervise their minor children. And in many of those states, when the parent (or legal guardian) fails to provide adequate supervision, so that the child ends up harming another person or causing damage to someone else's property, the parent/guardian can be held legally responsible. Usually that means the parent/guardian is on the financial hook for the cost of the damage (up to certain dollar limits).

These laws (collectively known as "parental responsibility laws") typically apply to intentional acts committed by a child (including theft, vandalism, and assault). In some states, parents can even be liable for accidents caused by their children -- including traffic accidents, especially when the parent/guardian gave a teen driver permission to use the family vehicle. 

For the details on parental responsibility laws in your state, choose a link from the list below.