This is the statute of the Torah that the Lord has commanded, saying: Speak to the children of Yisrael, and they shall take to you a red heifer, perfect, in which there is no blemish, and upon which a yoke has not been laid.
Torah Temimah: Sifrei — R. Eliezer: “Chukas” is said here and “chukas olam” is said there (Acharei); just as there [Yom Kippur] it is in white garments, so here [para aduma] it is in white garments.
English: It was taught: R. Eliezer says, “Chukas” is said here and “chukas olam” is said there; just as there it is in white garments, so here it is in white garments.
Gezeirah shavah on the word “chukah” linking the garments of the para service to those of Yom Kippur.
The Kohen who performs the para aduma service wears the same white garments used by the Kohen Gadol on Yom Kippur, not the golden garments.