Being from California myself, I can pretty much assure you that shooting your bow in your backyard is illegal. That said, it's pretty low on any law enforcement priority list of things to look into, unless someone complains or you accidently shoot someone, their dog, or their car. Then it can jump up on the law-enforcement priority list real fast. Your neighbors are going to find out that you shoot the bow in your backyard, so I hope you have as good-hearted neighbors as I do, who have known for years that I shoot the bow in my backyard and don't care. Make sure your targets are well-backstopped, and I always plan my shooting for times when my neighbors are not out in their backyards, because I don't want to push that good-heartedness too much.
Obviously, if I lived in one of the more metropolitan areas of California, the rules might be different and I wouldn't be able to get away with shooting arrows in my backyard, period, but then again, that's why I don't live there.