Reference for Zevachim 12:4

התם נמי כיפר מתן בהונות לא כיפר מתנות הראש

Shall we say, that he must bring another sacrifice? But you say, 'Whether he did put or he did not put, he made atonement'! Hence it must mean, 'It made atonement' - for the person, 'yet it did not make atonement' - before Heaven.

Jastrow