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I doubt it's specifically a crime under American law either. What's your point?

Laws will vary by state but this is in the Texas penal code:

§ 42.08. Abuse of Corpse
(a) A person commits an offense if, not authorized by law, he intentionally or knowingly:
(1) disinters, disturbs, removes, dissects, in whole or in part, carries away, or treats in a seriously offensive manner a human corpse;
(2) conceals a human corpse knowing it to be illegally disinterred;
(3) sells or buys a human corpse or in any way traffics in a human corpse; or
(4) transmits or conveys, or procures to be transmitted or conveyed, a human corpse to a place outside the state.
(b) An offense under this section is a Class A misdemeanor.
Acts 1973, 63rd Leg., p. 883, ch. 399, § 1, eff. Jan. 1, 1974. Renumbered from § 42.10 by Acts 1993, 73rd Leg., ch. 900, § 1.01, eff. Sept. 1, 1994.

It can cover grave robbing, necrophilia, and cannibalism (of a dead body).

Additionally the sale of human flesh (tissue) is prohibited:

§ 48.02. Prohibition of the Purchase and Sale of Human Organs
(a) "Human organ" means the human kidney, liver, heart, lung, pancreas, eye, bone, skin, fetal tissue, or any other human organ or tissue, but does not include hair or blood, blood components (including plasma), blood derivatives, or blood reagents.
(b) A person commits an offense if he or she knowingly or intentionally offers to buy, offers to sell, acquires, receives, sells, or otherwise transfers any human organ for valuable consideration.
(c) It is an exception to the application of this section that the valuable consideration is: (1) a fee paid to a physician or to other medical personnel for services rendered in the usual course of medical practice or a fee paid for hospital or other clinical services; (2) reimbursement of legal or medical expenses incurred for the benefit of the ultimate receiver of the organ; or (3) reimbursement of expenses of travel, housing, and lost wages incurred by the donor of a human organ in connection with the donation of the organ.
(d) A violation of this section is a Class A misdemeanor.
Added by Acts 1985, 69th Leg., ch. 40, § 1, eff. Aug. 26, 1985. Amended by Acts 1993, 73rd Leg., ch. 900, § 1.01, eff. Sept. 1, 1994.

I doubt it's specifically a crime under American law either. What's your point?

Don't most states have laws about proper disposal of bodies?