Tosefta על חולין 268:42

[The laws pertaining to the priestly gifts of] "the shankbone, the cheeks, and the maw" (Deut. 18:3) apply to kilayim (the mixed-breed offspring of two kosher animals) as well as to a k'vi. Rabbi Eliezer says, as to kilayim, it applies to [the offspring of] a ewe and a goat, but as to a k'vi, the burden of proof lies with the claimant. One who slaughters for medicinal purposes, to feed idolaters, or to feed dogs is liable in the gifts. One whose slaughter renders the animal carrion, one who ripped open [or] tore loose [the gullet or windpipe], and the slaughter of an idolater are exempt from the gifts. A Kohen and an idolater that sold their animal to an Israelite to slaughter are liable in the gifts, [but if it] was slaughtered with their permission and afterwards he sold it, he is exempt from the gifts. An Israelite that sold his animal to a Kohen to slaughter is exempt from the gifts, [but if it] was slaughtered with his permission and afterwards he sold it, he is liable in the gifts.

A Kohen is exempt and one who partners with a Kohen [in the profits from an animal] is exempt. An idolater is exempt. One who partners with an idolater is exempt. One who partners with a Kohen needs to make a mark [on the animal]. [One who partners] with an idolater does not need to make a mark, and [as to any animal that is] disqualified from being consecrated, one need not make a mark. [If] a Kohen said to him, "Everything is yours but the foreleg is mine," even [if he said it as to only] one [animal] in a hundred, he is exempt from the [gift of the] shankbone. [If a Kohen said to him,] everything is yours but the intestines are mine, even [if he said it as to only] one [animal] in a hundred, he is exempt from the [gift of the] maw. In a place where they are accustomed to skin the head [of an animal], they are not permitted to skin the cheeks, and [in a place where they are accustomed to] scald a calf [in boiling water], they are not permitted to scald the shankbone and if there is a Kohen [nearby], they give [the priestly gifts] to the Kohen, and if not, they convert [their value] to money [and give the money to a Kohen when one is found]. § [If a butcher] sold the foreleg as it is (i.e., fully intact), the head as it is, or the intestines as they are -- they give [the gifts] to the Kohen, and they do not deduct their value from what they owe to the butcher. [If] they bought by weight, they give [the gifts] to the Kohen and they may deduct their value from what they owe to the butcher. § The gifts do not have any holiness, and they may even be sold [by the Kohen] to an idolater, or even given to his dog. They are not subject to any commandment except to give them to the Kohen. § One who sends meat to his fellow, and and there were gifts in it, they need not be concerned lest they are priestly gifts.