Whenever the Altar does not acquire the right to the meat, the Kohanim do not acquire the right to the hide; as it is said (Lev. 7:8): [The Kohen who offers] a person’s olah offering — an olah which has been credited to a person. An olah-offering which was slaughtered for a designation other than its own, even though it is not credited to its owner, its hide [belongs] to the Kohanim. Both the olah-offering of a man and the olah offering of a woman — their hides [belong] to the Kohanim.