Related על כתובות 51:15

And similarly with two men—this one says, "My fellow is a kohen" and the other one says, "My fellow is a kohen"—they give to them [the priestly gifts]; but for priestly pedigree [i.e. to pass onto their children] they are not believed until there are 3 men, in order that 2 of them testify about the 3rd and the other 2 testify about the other 3rd. Rabbi Yehudah says: They don't even give them [the priestly gifts] until there are 2 to testify about this one and 2 to testify about this one. They raise someone to the priesthood, to being a Levite or an Israelite on the basis of one witness; but they do not lower someone except on the basis of 2 witnesses. Rabbi Yehudah says: Just as they don't lower someone except on the basis of 2, they don't raise except on the basis of 2.

There are 2 grounds for presumption of being a priest in Eretz Yisrael: doing the priestly blessing and taking one's portion from the threshing floor. But in Suria and until the place that the Rosh Hodesh heralds arrive, doing the priestly blessing [is a ground for presumption] but not taking one's portion from the threshing floor. Bavel is like Suria. Rabbi Shimon ben Lazar says: Also in Alexandria originally, since there was a court there. Rabban Shimon ben Gamliel says: Just as terumah is a ground for presumption for being a priest when one takes it from the threshing floor, so too is first tithe a ground for presumption for being a Levite when one takes it from the threshing floor. One who takes his portion in a court does not have grounds for presumption to being a priest.