What was the responsibility of the priest when he was the one bringing the offer?
Leviticus 4:4 (ESV)
4He shall bring the bull to the entrance of the tent of meeting before the LORD and lay his hand on the head of the bull and kill the bull before the LORD.
It is important to note that on this occasion, the anointed priest takes on the position of the worshipper. The worshipper was to kill the animal in the presence of the Lord.
4 He shall bring the bull to the entrance of the tent of meeting before the LORD and lay his hand on the head of the bull and kill the bull before the LORD.