Under the Law Atonement by Priests Alone
Source: TTT
1 Chronicles 6:49
But Aaron and his sons did all the work of the Most Holy Place. They presented the offerings on the altar of burnt offering and on the altar of incense to make atonement for Israel, according to all that Moses the servant of God had commanded.
2 Chronicles 29:24
And the priests slaughtered the goats and put their blood on the altar for a sin offering, to make atonement for all Israel, because the king had ordered the burnt offering and the sin offering for all Israel.