What amputated or removed organs, not limited to limbs, are hospital patients NOT allowed to take home in the U.S.? If the laws vary between states, then I'll focus on Washington State.
I should have read the article more closely before posting my question. This is apparently the answer:
Most hospitals have policies where they will release your body parts to you because of some religions where you have to be buried whole.
So if, for some reason, you want to keep your amputated arm or gall bladder, you could presumably tell the hospital administration that your religious beliefs require you to be buried whole.
I'm not sure if it's really that cut and dried, though. Do they ask you to specify a religion, for example?