TT #373 · Parashas Shoftim · Seventh Aliyah · Passuk 21:05
And the kohanim, the sons of Levi, shall approach, for them the Eternal your God has chosen to serve Him and to bless in the name of the Eternal, and according to their word shall be every dispute and every plague.
Torah Temimah points to Sifrei Devarim 208.
TT lemma: וְעַל פִּיהֶם יִהְיֶה כׇּל רִיב וְכׇל נָגַע.
English: ‘And according to their word shall be every dispute and every plague’ – to teach that they are appointed over judgments.
Derash on judicial authority (Sifrei) — the same verse that places kohanim at the eglah also affirms their role in Torah decisions.
The kohanim’s presence at the eglah arufah is of a piece with their broader authority in matters of dispute and purity.