מדרש על במדבר 18:7

2) "and he shall slaughter": This teaches us that shechitah is kasher with zarim (non-Cohanim), women, bondsmen, and the unclean, even with higher-order offerings, so long as the unclean do not touch the flesh. Or, perhaps only a Cohein may perform shechitah! — Now, "where are you coming from?" (i.e., What is your source?) From (Bamidbar 18:7): "And you and your sons with you shall guard your priesthood for all that pertains to the altar." I might think that this includes shechitah. But (Vayikra 1:5): "And the sons of Aaron, the Cohanim, shall present the blood, and they shall dash the blood, etc." indicates that from this point on (i.e., receiving the blood) is the mitzvah of the priesthood; but shechitah is kasher with all persons.