Do Zombies Have Civil Rights?

Here's an interesting question that I hope never comes up in real life:

Do Zombies Have Civil Rights?

Sure Zombies have died and re-animated, but so have countless heart attack victims.  They may be dead, but they also have brain activity.  Something powers the zombie.  They may not have traditional intelligence as we know it, but neither do plenty of head trauma and stroke victims.  If they have brain activity, then killing them may not be legal.  

Zombie Photo - By Hypnotica Studios Infinite from Toms River, New Jersey, USA (Asbury Park Zombie Walk 2010) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

I'm no lawyer, but from a legal perspective, authorities may need to capture Zombies and provide them with some sort of medical treatment.  Zombies already have a tongue in cheek advocacy group:  The Zombie Rights Campaign. It's something to think about!