First caveat, this applies to Washington law only, zombie hunter/killers in other states beware of relying on the opinions here.
Second caveat, you are not law enforcement. You have taken upon yourself to rid the State of Washington of these undead parasites.
Third caveat, zombies are not people. The law in Washington defines person as: "Person", "he", and "actor" include any natural person and, where relevant, a corporation, joint stock association, or an unincorporated association. RCW 9A.04.110(17). While zombies may be people (and maybe more of a person than some corporations like Google and BP), they clearly aren't "natural" so in Washington, zombies aren't people.
So, what happens to you when you, full of righteous fury, blow an attacking zombie's head off? The police come and arrest you. "But," you stutter to the officer, "I was acting in self-defense!" Ah, well there's the rub. In Washington you can legally use force to defend yourself against a person. And as shown above, in Washington, zombies are not people. You would be guilty of Unlawful Disturbance of Human Remains, RCW 68.50.140(4) Every person who removes, disinters, or mutilates human remains from a place of interment, without authority of law, is guilty of a class C felony. While you might be able to get a jury to nullify your case with a good attorney, you are certainly taking a risk 12 gauging that undead hellspawn.
But remember: Its better to be judged by twelve than carried by six or, in the case of zombies, to walk forever the earth as undead scum.