Zevachim 12:3: The hides of Kodashim Kalim [sacrifices of a lesser degree of sanctity. They may be slaughtered anywhere in the Temple courtyard and consumed by most anyone, anywhere in Jerusalem] [are given] to its owners, but the hides of Kodshai Kodashim [sacrifices of the highest degree of sanctity. They may be slaughtered only on the north-west corner of the altar, and consumed only within the Temple compound by male priests, or burnt entirely] [are given] to the priests. [This can be shown through] a Kal Vachomer [a fortiori reasoning]: If [priests], who do not have rights to meat from an Olah, do have rights to its hide, is it not logical that they should have rights to the hides of [other] sacrifices of Kodshai Kodashim [considering] that they do have rights to their meat? [And] the altar cannot prove [otherwise] because it never [receives] any hide.

עורות קדשים קלים לבעלים, ועורות קדשי קדשים לכהנים. קל וחמר, מה אם עולה שלא זכו בבשרה זכו בעורה, קדשי קדשים שזכו בבשרה אינו דין שיזכו בעורה. אין מזבח יוכיח, שאין לו עור מכל מקום.

Zevachim 12:4: [If] a sacrifice became invalid before it was skinned, its hide is not [given] to the priests; [if it became invalid] after it was skinned, its hide is [given] to the priests. Rabbi Chanina Segan HaKohanim said: In my life I never saw a hide [be taken] out [of the Temple precincts] to be burned. Rabbi Akiva said: From his statement we learn that [if] one skins a Bechor [first-born offering] which was [then] found to be a Terefah [an animal with a mortal condition such that it would die within one year], the priests should still benefit from its hide. And the Sages say: [The statement of] "we never saw" is no proof; rather [the hide] goes out to the place of burning.

כל הקדשים שארע בהם פסול קדם להפשטן, אין עורותיהם לכהנים. לאחר הפשטן, עורותיהם לכהנים. אמר רבי חנינא סגן הכהנים: מימי לא ראיתי עור יוצא לבית השרפה. אמר רבי עקיבא: מדבריו למדנו, שהמפשיט את הבכור ונמצא טרפה, שיאותו הכהנים בעורו. וחכמים אומרים: אין לא ראינו ראיה, אלא יוצא לבית השרפה.