Taharos, Chapter 5, Mishnah 8. Our chapter deals with doubtful tumah, and this mishnah asks how the presence of certain people in a town affects everything found lying in its streets, and how a person should handle an encounter with a woman whose status he does not know.
The mishnah begins: "Shotah achas ba'ir, o nochris, o Chusis, kol harukin sheba'ir temei'in." If there is a single madwoman in the town, or a non-Jewish woman, or a Chutis, then all spittle found in that town is tamei.
Why these three? A shotah, a woman who is not of sound mind, is not relied upon to track her niddah cycle or to tend to it properly, so she is presumed to be a niddah. Note that the shotah in the mishnah is specifically a woman. Non-Jews and Chutim, on the other hand, whether male or female, were given the status of zavim by rabbinic decree as a matter of course. Any one of them living in the town is enough to render every piece of spittle found there suspect, since we must be concerned that it came from that person.
A word about the Chutim: these are the Samaritans, the population settled in the north of Eretz Yisrael. They accepted Judaism out of fear of the lions that were attacking them, and the Sages were never settled on whether such a conversion could be considered valid. As a result they occupied an odd intermediate category, treated as Jews for certain matters and as non-Jews for others. For our halachah they are grouped together with non-Jews.
A remark on the scenario itself: the point is not that such individuals are unusually prone to spitting. Rather, in that era saliva on the ground was apparently encountered often enough in a public thoroughfare that ruling on its purity was a genuine everyday concern.
The mishnah continues with a second situation: "Mi shedarsah ishah al begadav, o sheyashvah imo bisefinah." A woman trod on a man's garments, or she sat down together with him in a boat. These are exactly the kinds of contact that would transmit midras tumah if she were a niddah. She is a woman he does not know, he did not ask her anything, and now he must decide whether he and his clothing are tamei.
The mishnah's answer turns on whether she knew who he was. "Im makirah oso shehu ochel biterumah, kelav tehorin." If she recognizes him as someone who eats terumah, meaning he is the known kohen of the town, his garments remain tahor. We may assume that a woman who is aware of who he is would not have trodden on his clothing or seated herself beside him in a boat had she been a niddah; she would have been considerate enough to keep her distance.
"Ve'im lav, yish'alenna." But if she does not know him and has no reason to identify him as someone who eats terumah, no such assumption can be made. He cannot rely on the general carefulness of strangers, and he must go and ask her directly what her status is. And, as with anything of this nature, he should ask in the most delicate and respectful manner he can.