Hilchos Maasei Hakarbanos 5:19

All hides of sacrifices of the highest sanctity are given to the kohanim – both those of communal offerings and those of private offerings. This is as per Leviticus 7:8: “The hide of the burnt offering that he brought (will belong to the kohein).” The hides of sacrifices of lesser sanctity are given to the owners of the offerings. If the flesh of a burnt offering isn’t able to be burned on the altar (because it was disqualified), the kohanim do not receive the hide, as per the aforementioned verse, which says, “the burnt offering of a person.” It has to be a burnt offering that counted for a person.

Hilchos Maasei Hakarbanos 5:20

If the thing that disqualified the offering happened to an offering of the highest sanctity before it was skinned, the hide is not given to the kohanim. If it was disqualified after it was skinned, then the hide is given to the kohanim. All the hides are divided among the members of the kohanim on the duty roster from one Friday to the next.