The owners of household pets are responsible for their animals. Most local cities and towns have leash laws or other dog control statutes, including those that prohibit the harboring of dangerous animals like pit bulls and Rottweilers. Generally, you must first demonstrate that that animal has dangerous tendencies, which usually requires that you show that the dog has exhibited prior behavior that could be considered dangerous to humans. The mere barking or growling of a dog is not sufficient to impose liability on the landowner. Dog bite claims are covered under the pet owner's homeowners insurance, and insurance companies typically deny these claims until an attorney becomes involved.
If you or a member of your family is involved in such a dog attack, be sure to learn the name of the dog, report it to Animal Control and find out if the pet owner has homeowners insurance; then consider seeking the help of a lawyer.