Yevamos, Chapter 3, Mishnah 8. Already in the opening mishnah of the tractate we learned that the fifteen forbidden relatives who are exempt from yibum also exempt their co-wife - the additional wife of their husband. Our mishnah deals with situations in which it is not at all clear that these women are in fact co-wives.
The words of the Mishnah:
The Mishnah rules: "V'chol sheyecholos bahen kiddushin v'gerushin b'safek - harei elu tzaros cholatzos v'lo misyabmos" - and in every case where the validity of the kiddushin or of the divorce is in doubt, these co-wives perform chalitzah but do not undergo yibum. There are two types of doubt before us:
Doubtful kiddushin: It is uncertain whether they were married at all, since perhaps the kiddushin never took effect, and consequently there is no certainty that they are co-wives of the husband's other wife.
Doubtful divorce: They were certainly married, but afterward they were given a get whose validity is in doubt. Since the get was given before the husband died, this affects whether they are defined as co-wives with regard to yibum.
Why they perform chalitzah but not yibum:
In circumstances of doubt, the co-wives perform chalitzah and do not undergo yibum, because the doubt pulls in both directions:
If they really were co-wives of a forbidden relative, they are exempt from yibum and it is impossible to perform yibum with them. In such a case she has the status of a brother's wife, like the widow of a brother who had children, who is a forbidden relative.
And if they are not co-wives of a forbidden relative, they are obligated in yibum, and therefore chalitzah must be performed.
What is a case of doubtful kiddushin:
The Mishnah asks: "Keitzad safek kiddushin?" - what is a case of doubtful kiddushin? And it answers: "Zarak lah kiddushin, safek karov lo safek karov lah" - the man threw the money of kiddushin to the woman, and a doubt arose as to whether the ring landed closer to her or closer to him.
This scenario necessarily refers to a case where the two of them are standing in a public domain with exactly eight amos separating them. The rule is that whatever is within a person's four amos is within his domain, and his four amos acquire it for him. Here the kiddushin landed exactly in the middle, on the dividing line, and therefore it is uncertain whether it reached her domain and her area or not, and consequently it is uncertain whether the kiddushin took effect. "Zehu safek kiddushin" - this is a case of doubtful kiddushin.
What is a case of doubtful divorce:
Although in principle the very same problem could arise with divorce as well, in the throwing of a get to the woman, the Mishnah takes a different example. Here it is not a genuine doubt, but rather a get that was not made in the proper manner. The Mishnah lists three examples:
"Kesavo b'chsav yado v'ein alav eidim" - the husband wrote the get in his own handwriting, and there are no witnesses on the get. His handwriting has a certain validity as a get, but this is not the correct way to make a get.
"Yesh alav eidim v'ein bo zman" - there are witnesses signed on the get, but no date was written in it, and the Sages instituted that a get must contain a date.
"Yesh bo zman v'ein bo ela ed echad" - a date was written in it, but only one witness is signed on it.
The halachah in these three cases is that all of these gittin are invalid - invalid by rabbinic enactment. But after the fact, if the woman remarried on the basis of one of these gittin and had a child, the child is legitimate. And the Mishnah concludes: "Zehu safek gerushin" - these are the examples of a doubt as to whether the get is valid or not.
In summary: In this mishnah we learned that when there is a doubt about the kiddushin itself or about the validity of the get, there is no certainty whether we are dealing with the co-wife of a forbidden relative who is exempt from yibum or with a woman who is obligated in it, and therefore the co-wives perform chalitzah and do not undergo yibum. We saw the Mishnah's example of doubtful kiddushin - throwing the kiddushin so that it is uncertain whether it landed closer to him or closer to her - and the three examples of doubtful divorce: a get in his handwriting without witnesses, a get with witnesses but without a date, and a get that has a date but only one witness.