In most cases, yes. In Washington state, there is a state law that imposes strict liability (i.e., absolute responsibility regardless of the circumstances) for bites against the animal’s owner.
In most situations, the homeowner's insurance policy would be the primary source of financial recovery for a dog bite case. The requirement is that the bite occur on public property - or on private property with the owner’s consent - and that the animal was not provoked.
In other situations, the dog owner may be liable if you can show that the owner knew his/her dog had aggressive or violent tendencies but failed to quarantine the animal or protect people it came in contact with, or if the owner had knowledge that the animal had previously bitten another person.
For dog bites that result in serious, long-term injuries, the injury victim may benefit from consulting with a personal injury attorney who has experience in handling dog bite claims. A lawyer who has experience in this area of the law will be better suited to identify the many complex issues that may arise throughout the personal injury legal process.