Тосефта к Бамидбар 19:3

וּנְתַתֶּ֣ם אֹתָ֔הּ אֶל־אֶלְעָזָ֖ר הַכֹּהֵ֑ן וְהוֹצִ֤יא אֹתָהּ֙ אֶל־מִח֣וּץ לַֽמַּחֲנֶ֔ה וְשָׁחַ֥ט אֹתָ֖הּ לְפָנָֽיו׃

И вы отдадите ее Елеазару священнику, и она будет выведена без стана, и она будет убита пред лицем его.

Tosefta Parah

Rabbi Yosei HaGalili says, the burnt offerings that our forefathers brought on Mount Sinai did not require flaying and cutting [into pieces]; rather, from the giving on the Torah and thereafter. The burning of the heifer and her sprinkling [are performed] by the High Priest, and the remaining [rituals are performed] by an ordinary Kohen, as it is said (Num. 19:3), "And you shall give it to Elazar the Kohen." Elazar, who was the deputy [to Aaron, the High Priest], and [thus the rituals involving] the subsequent heifers [are performed] by an ordinary Kohen, the words of Rabbi Meir. Rabbi Yosei son of Rabbi [Yehuda] and Rabbi Shimon and Rabbi Eliezer ben Ya'akov say, that one [was performed] by Elazar, who was the deputy, but [the rituals involving] all the subsequent heifers -- even the High Priest [may perform them].