Can I kill My Neighbors Pet if it is on my proerty?

Im 14 and don't know much about laws that have to do with dogs. So amyways I was at my grandmas house and she is 76. Her daughter is 51 but she has an epilepsi so she has seizures and is not capable of living on her own because she would die.I live in Lps Angeles California and her neighbor on her left has bunnies and she let's them run Free. So I've seen one get run over. But anyways I caught one doing poop in her yard and she cant see very well so she can't pick it up. She is alsp diabetic and.I'm not trying to be mean but she is fat but most diabetic people are. My aunt went to college and everything but overtime she became stupid. So amyways now the neighbor on the right has a chihuaha or chiwawa I don't know how to spell it but it also poops my grandmas lawn. So is it legal to kill there dog in CA or can i sue them