מדרש אויף ויקרא 4:35

3) (Vayikra 4:33): "And he shall place his hand on the head of the sin-offering" — to include for semichah: the sin-offering of the Nazirite, of the leper, and of the defiler of the sanctuary. "And he shall slaughter it as a sin-offering" — expressly as a sin-offering. (Vayikra 4:34): "And the Cohein shall take from the blood of the sin-offering" — expressly for a sin-offering. (Vayikra 4:35): "And the Cohein shall atone for him for his sin" — expressly for his sin. — whence they said: If (in sacrificing a sin-offering), he did not slaughter it, or receive (the blood), or bring it (on the altar), or sprinkle it — to that end — it is pasul.

4) (Vayikra 4:35): "And all its fat he shall remove, as the fat of the lamb is removed from the sacrifice of the peace-offerings." What is removed in the sacrifice of the peace-offerings? The fat that is an even layer, membranous, and easily peeled, and the two kidneys and the lobe. Here, too, (the same is removed).

5) "and the Cohein shall make atonement for him": (This teaches us that) the atonement must be expressly for him (the owner of the offering), that he not atone for two at one time (by mixing the blood of the two offerings), and that the Cohein (performing the service) may atone for himself (i.e., It is not necessary that another Cohein perform the service for him.) "and it shall be forgiven him": his sin is not left "suspended" until Yom Kippur, (but he is forgiven completely). I might think that even if he (the Cohein) "sat" and did not offer it (the owner nevertheless receives atonement); it is, therefore, written ("and it shall be forgiven) him" (i.e., only him for whom the service has been performed.)