Mishnah Parah 2:3: One [a red heifer] born through a Caesarean section [literally: came out through a wall], one given as payment [for a harlot], or as a price [for a dog] are invalid. Rabbi Eliezer validates [them], as the verse says: (Deuteronomy 23:19) "Do not bring a harlot's payment or the price of a dog to the house of Hashem your G-d," and this one, [the red heifer,] does not come to the house. All the blemishes which invalidate sacrifices invalidate the [red] heifer. [If] one rode on it, leaned on it, hung from its tail, used it to cross a river, doubled the reins over it, [or] placed his cloak on it, it is invalid. But if he tied it with a rein, made a shoe for it to prevent slipping, [or] spread his cloak over it because of the flies, it is valid. This is the rule: anything [done] for its own needs [that of the heifer], it is valid. For any other needs, it is invalid.

יוֹצֵא דֹפֶן וְאֶתְנָן וּמְחִיר, פְּסוּלָה. רַבִּי אֱלִיעֶזֶר מַכְשִׁיר, שֶׁנֶּאֱמַר (דברים כג), לֹא תָבִיא אֶתְנַן זוֹנָה וּמְחִיר כֶּלֶב בֵּית ה' אֱלֹהֶיךָ, וְאֵין זוֹ בָאָה לַבָּיִת. כָּל הַמּוּמִים הַפּוֹסְלִים בַּמֻּקְדָּשִׁים, פּוֹסְלִים בַּפָּרָה. רָכַב עָלֶיהָ, נִשְׁעַן עָלֶיהָ, נִתְלָה בִזְנָבָהּ, עָבַר בָּהּ אֶת הַנָּהָר, קִפֵּל עָלֶיהָ אֶת הַמּוֹסֵרָה, נָתַן טַלִּיתוֹ עָלֶיהָ, פְּסוּלָה. אֲבָל קְשָׁרָהּ בַּמּוֹסֵרָה, עָשָׂה לָהּ סַנְדָּל בִּשְׁבִיל שֶׁלֹּא תַחֲלִיק, פָּרַס טַלִּיתוֹ עָלֶיהָ מִפְּנֵי הַזְּבוּבִים, כְּשֵׁרָה. זֶה הַכְּלָל, כֹּל שֶׁהוּא לְצָרְכָּהּ, כְּשֵׁרָה. לְצֹרֶךְ אַחֵר, פְּסוּלָה:

Mishnah Parah 2:4: If a bird rested on it, it is valid. If a male mounted it, it is invalid. Rabbi Yehudah says: If one caused [the male] to mount, it is invalid. If [it mounted] on its own accord, it is valid.

שָׁכַן עָלֶיהָ עוֹף, כְּשֵׁרָה. עָלָה עָלֶיהָ זָכָר, פְּסוּלָה. רַבִּי יְהוּדָה אוֹמֵר, אִם הֶעֱלָהוּ, פְּסוּלָה. וְאִם מֵעַצְמוֹ, כְּשֵׁרָה: