Zevachim 12:3-4

Zevachim 12:3

The hides of kodshim kalim (sacrifices of lesser sanctity) belong to the owners, while those of kodshei kodashim (sacrifices of greater sanctity) belong to the kohanim. This is based on a kal v’chomer (an argument a fortiori): if the kohanim receive the hide of a burnt offering, whose meat they do not receive, certainly they should receive the hides of kodshei kodashim, whose meat they do receive. The fact that the altar receives the meat of burnt offerings but not the hides does not affect this argument because hides are never burned on the altar.

Zevachim 12:4

If sacrifices were invalidated before they were skinned, the hides do not belong to the kohanim; after they were skinned, the hides do belong to the kohanim. Rabbi Chanina the Deputy High Priest said that he never saw a hide taken out to the place of burning (so, presumably, all hides were given to the kohanim). Rabbi Akiva derived from Rabbi Chanina’s statement that if one skins a firstborn animal and it is found to be a treifa, the kohanim may use the hide. The Sages, however, say that Rabbi Chanina’s failure to see something doesn’t mean that it never happened. Rather, such hides were in fact taken out to the place of burning.