Related for Kiddushin 4:4
הַנּוֹשֵׂא אִשָּׁה כֹהֶנֶת צָרִיךְ לִבְדֹּק אַחֲרֶיהָ אַרְבַּע אִמָּהוֹת שֶׁהֵן שְׁמֹנֶה, אִמָּהּ וְאֵם אִמָּהּ, וְאֵם אֲבִי אִמָּהּ וְאִמָּהּ, וְאֵם אָבִיהָ וְאִמָּהּ, וְאֵם אֲבִי אָבִיהָ וְאִמָּהּ. לְוִיָּה וְיִשְׂרְאֵלִית, מוֹסִיפִין עֲלֵיהֶן עוֹד אֶחָת:
If one (a Cohein) wishes to marry the daughter of a Cohein, he must examine her lineage four mothers back, [two on the father's side, two on the mother's], who are eight; [four on the father's side, four on the mother's], viz.: her mother, her mother's mother, her mother's father's mother, the mother [of her mother's father's mother]; her father's mother, her father's mother's mother, her father's father's mother, the mother [of her father's father's mother]. They are examined for possible p'sul (unfitness)]. [If a Cohein wishes to marry] the daughter of a Levite or an Israelite, one is added [i.e., one mother in each set, viz.: her mother, her mother's mother, her mother's mother's mother — and so with all. The reason the mothers are examined for p'sul and not the fathers, (e.g., her father or her father's father) is that men tend to revile each other with (imprecations of) tainted pedigree in quarreling, so that if there were a p'sul in one of the fathers it would have become known. But women revile each other not with tainted pedigree but with z'nuth (accusations of harlotry), so that if one of them were thus tainted, it would not have become known (in their quarreling). And this requirement of examination is stated only in regard to a family which has come under suspicion, but in the absence of such suspicion, no examination is necessary, for all families are in the status of kashruth. And it is only the man who must conduct this examination when he wishes to marry a woman from a family that has come under suspicion. But the daughter of a Cohein need not examine the (lineage of the) man she wishes to marry, for women who are kasher were not exhorted against marrying men who are pasul — so that the daughter of a Cohein (and, it goes without saying, the daughter of a Levite or an Israelite) may ab initio marry a proselyte or a challal.]