משנה אויף במדבר 19:1

If a hatat cow was slaughtered not for its own name, or if its blood was received or sprinkled not for its own name, or if this was done for its own name and for some other name, or for some other name and for its name, it is invalid. Rabbi Eliezer rules it valid. If [the service] was performed by one whose hands or feet were unwashed, it is invalid. Rabbi Eliezer rules that it is valid. If it was performed by one who was not the high priest, it is invalid. Rabbi Judah rules that it is valid. If it was performed by one who was not wearing all the prescribed garments, it is invalid. And in white garments it was to be prepared.

The one who burns the red cow or bulls and he that leads away the scapegoat, defile garments. The red cow and the bulls and the scapegoat do not themselves defile garments. Behold [the garment] would say [to the person], "That which defiled you did not defile me, but you did defile me.