Tosefta for Chullin 1:4
הַשּׁוֹחֵט מִן הַצְּדָדִין שְׁחִיטָתוֹ כְשֵׁרָה. הַמּוֹלֵק מִן הַצְּדָדִין, מְלִיקָתוֹ פְסוּלָה. הַשּׁוֹחֵט מִן הָעֹרֶף, שְׁחִיטָתוֹ פְסוּלָה. הַמּוֹלֵק מִן הָעֹרֶף, מְלִיקָתוֹ כְשֵׁרָה. הַשּׁוֹחֵט מִן הַצַּוָּאר, שְׁחִיטָתוֹ כְשֵׁרָה. הַמּוֹלֵק מִן הַצַּוָּאר, מְלִיקָתוֹ פְסוּלָה, שֶׁכָּל הָעֹרֶף כָּשֵׁר לִמְלִיקָה, וְכָל הַצַּוָּאר כָּשֵׁר לִשְׁחִיטָה. נִמְצָא, כָּשֵׁר בִּשְׁחִיטָה, פָּסוּל בִּמְלִיקָה. כָּשֵׁר בִּמְלִיקָה, פָּסוּל בִּשְׁחִיטָה:
An animal which was slaughtered by being cut at either side of the throat is Cashér, but if the neck of a bird brought as a sacrifice was wrung off sideways, it is thereby rendered an unfit sacrifice. If an animal was cut from the neck downwards, it becomes unlawful for use, but a bird whose neck was thus wrung is a valid sacrifice. An animal which was cut below the throat is Cashér, but the wringing off of birds’ heads from below the throat render them unfit sacrifices, because the whole region of the neck is appropriate for the wringing off of the head [of birds], and the whole region of the throat for slaughtering [animals], therefore whatever [in respect to cutting] renders an animal Cashér, must render a bird thus treated an unfit sacrifice, and the same in the reverse case.