Leviticus 5:7-8

7‘But if he cannot afford a lamb, then he shall bring two turtledoves or two young pigeons as his guilt offering for his sin to the Lord, one as a sin offering and the other as a burnt offering.

8He shall bring them to the priest, who shall offer first the one for the sin offering, and shall nip its head at the front of its neck, but shall not sever it [completely].