Torah Temimah cites Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10).
Sefaria — Toras Kohanim (Sifra, Vayikra Dibbura DeChovah, Section 10)
“He shall make it an olah according to the rule” — according to the rule of the bird-chatas: just as the bird-chatas is nipped from opposite the nape, so too the bird-olah.
Hekesh of the companion olah bird to the chatas bird via “ka-mishpat.”
Both birds of the pair are killed by melikah from the nape. The olah follows the same bird-procedure as its chatas partner; the Torah does not require a different method of slaughter for the second bird.