Yevamos, Chapter 2, Mishnah 9. This mishnah deals with several additional cases in which a person who gives testimony that permits a woman to remarry may not marry her himself, lest he be suspected of having testified only in order to permit her to himself.
"Hameivi get mimedinas hayam":
The mishnah says: "Hameivi get mimedinas hayam ve'amar befanai nichtav uvefanai nechtam" - one who brings a get from overseas, from outside Eretz Yisrael, and testifies about the get that it was written in his presence and signed in his presence. The halachah is that a get coming from outside Eretz Yisrael requires testimony from those who saw it written and saw it signed.
Two reasons are given in the Gemara in Gittin:
People overseas were not necessarily expert in the requirement that a get must be written lishmah, for the sake of the particular woman for whom it is written. Since it is not clear that they understood this, the one delivering the get must testify that he was involved in the process - he saw it written and he saw it signed - and through this it becomes clear that it was written lishmah.
There is a concern that the husband may later come and claim that the get is forged, and therefore witnesses are required to testify that the signatures are genuine: I saw it written and I saw it signed.
Even though the get is valid on the basis of this statement, the one who testifies "lo yisa es ishto" - he may not marry this woman, since the matter looks suspicious, lest he did so only in order to permit her to himself.
Testifying about the husband's death:
Similarly, a person who gives testimony saying "meis" - that a married man died - or "haragtiv" - I killed him - or "haragnuhu" - that he and others killed him. A woman is permitted to remarry on the testimony of a single witness who says that her husband died, and here the witness indeed says that the husband died. However, if he is the source of this information, whether he was involved in the killing or whether he merely testifies that the man died, he may not marry the wife, for that same reason: we are concerned that perhaps he is not telling the truth, and that he is doing this only in order to marry her.
Rabbi Yehudah disagrees and distinguishes between the two expressions:
"Haragtiv": his wife may not marry at all, because according to his own testimony he is a wicked man, and he is neither trustworthy nor fit to testify.
"Haragnuhu": the meaning of this expression is not that he himself killed him, but that he was together with those people and was present at the time of the killing. Therefore his wife may marry, since he did not say that he was guilty of the murder, only that he was present at it.
The halachah in practice is that even if a person says that he himself carried out the murder, we do not believe him, because a person cannot render himself wicked - a person is not believed to say about himself that he is wicked. Therefore we split his testimony, by way of what the Gemara calls 'palginan dibura': he is believed to say that the other man died, and he is not believed regarding himself to say that he was the one who carried out the murder.
In summary: in this mishnah we learned two cases in which a person's testimony permits the woman to remarry, and nevertheless he may not marry her - one who brings a get from overseas and testifies "it was written in my presence and signed in my presence," and one who testifies about the husband's death with the words "he died," "I killed him," or "we killed him." We examined the two reasons for the testimony of "it was written in my presence and signed in my presence," Rabbi Yehudah's distinction between "I killed him" and "we killed him," and the halachah in practice that a person cannot render himself wicked and therefore we split his statement.