Reference for Chullin 166:24

מי לא תנן

it would indeed be so, but here [in our Mishnah] we are speaking of a bird consecrated for the Temple treasury.<span class="x" onmousemove="('comment',' Lit., 'for the repair of the House', i.e., for the general purposes of the Temple. As the slaughtering of this bird does not render it fit to be eaten, for it is forbidden for all purposes, the slaughtering is no slaughtering (v. supra ');">¹⁴</span>

Jastrow