Property damaged by a pet is generally considered negligence, rather than criminal, and thus payment to repair damage is a civil matter. If you fear the neighbor’s dog(s) getting into your yard, try fortifying your side of the fence to prevent them from doing so. Animal Control can also discuss options with your neighbors on ways to keep their dog(s) on their property. Until a dog has actually left its yard or injured another animal or human, charges generally are not able to be brought against its owner, i.e. no criminal laws have been broken.