If you shoot someone or they find it on you, the feds will work you over with so hard, you wish you were dead. The fact is that the national parks are a haven for criminals (similar to D.C., LA, Chicago and every other gun banned city). I refuse to go into the remote parts of the national park. The national forest on the other hand is just fine.
If you do carry and end up shooting, ahem, vermin in the national park, I believe it is best to bury dead animals so as to not attract other predators-namely the federal government.