According to Leviticus 4:6–7, Leviticus 4:17, the officiating priest was required to splatter the sacrificial blood in front of the veil of the sanctuary and pour the rest at the base of the altar. During this process some blood might splash onto the priest's clothes.
27 Whatever touches its flesh shall be holy, and when any of its blood is splashed on a garment, you shall wash that on which it was splashed in a holy place.