CITES listing is a way to determine wether an animal is protected. If something is highly protected then it is listed as CITES I. Owning or even sometimes selling these animals or parts is NOT always crime. Some people associate trading in protected species the same way as poaching or illegal trading, this is NOT always the case. As long as the correct paperwork is associated. in very short: CITES I means you need  official CITES documents. CITES II means you need to prove the origin of the specimen. No CITES means nothing on itself, it can be protected by other laws as well!

State laws can add to the CITES laws, For example some native songbirds are protected because they are native and are not protected by CITES. Others are not, if the animal is hunted in some times of the year, like foxes, crows pheasants deer or hares, the parts are not protected, because the meat in the freezer isn't protected either.