TT #389 · Parashas Shoftim · Seventh Aliyah · Passuk 21:08
Atone for Your people Yisrael whom You have redeemed, O Eternal, and do not place innocent blood in the midst of Your people Yisrael. And the blood shall be atoned for them.
Torah Temimah points to Sifrei Devarim 210.
TT lemma: וְנִכַּפֵּר לָהֶם הַדָּם.
English: ‘And the blood shall be atoned for them’ – from here that the blood is atoned.
Derash on the efficacy of the rite (Sifrei) — the Torah itself declares that the blood is atoned.
Once the eglah arufah has been performed and the prayers recited, the blood is atoned for the people.