Tossefta sur Le Deutéronome 12:21

כִּֽי־יִרְחַ֨ק מִמְּךָ֜ הַמָּק֗וֹם אֲשֶׁ֨ר יִבְחַ֜ר יְהוָ֣ה אֱלֹהֶיךָ֮ לָשׂ֣וּם שְׁמ֣וֹ שָׁם֒ וְזָבַחְתָּ֞ מִבְּקָרְךָ֣ וּמִצֹּֽאנְךָ֗ אֲשֶׁ֨ר נָתַ֤ן יְהוָה֙ לְךָ֔ כַּאֲשֶׁ֖ר צִוִּיתִ֑ךָ וְאָֽכַלְתָּ֙ בִּשְׁעָרֶ֔יךָ בְּכֹ֖ל אַוַּ֥ת נַפְשֶֽׁךָ׃

Trop éloigné du lieu choisi par l’Éternel, ton Dieu, comme siège de son nom, tu pourras tuer, de la manière que je t’ai prescrite, de ton gros ou menu bétail que l’Éternel t’aura donné, et en manger dans tes villes tout comme il te plaira.

Tosefta Chullin

Everyone is fit to slaughter, even a Samaritan, even an uncircumcised Israelite, and even an Israelite who changes his belief to idolatry (lit., "star-worship"). The slaughter by an idolater, behold, that is invalid, and the slaughter by a monkey, behold, that is invalid, as it is said, "And you shall slaughter…and you shall eat” (Deut. 27:7). Not that "the idolater shall slaughter," and not that "the monkey shall slaughter," and not that the slaughter shall be accidental. An Israelite that [commenced the] slaughter, and an idolater [who was] next to him finished the slaughter, the slaughter is invalid. If he slaughtered two [simanim (the gullet and the windpipe)], or the majority of two, his slaughter is valid. An idolater that [commenced the] slaughter, and an Israelite [who was] next to him finished the slaughter, the slaughter is valid. If [the idolater commenced the] slaughter with something that does not render [the slaughter] a tereifa*i.e., a mortal injuries or physical defect disqualifying an animal from consumption (see Hul. 3:1), and the Israelite came and finished, it is permitted to eat. An Israelite and an idolater that were holding the knife, and they slaughter -- even [if] one was on top and one was on the bottom (Hul. 2:2) -- their slaughter is valid.