Do you have to kill animals if you're a police officer?

I've heard you sometimes have to do things like shoot rabid/problem animals - is that true? I REALLY want to be an officer (my lifelong dream!), but I'm an animal lover. I know there are stories of officers having to kill mountain lions that get too close to civilization (among other stories) and I'm not willing to do that; is there any way to "opt out" if I'm ordered to kill an animal? I understand self-defense in extreme situations; I'm not talking about self-defense.