Shevuos, Chapter 4, Mishnah 7. This mishnah deals with cases in which the law of the oath of testimony does not apply, even though the witnesses were adjured to come and testify.
Testimony that does not involve a monetary claim:
A person says to potential witnesses: "Mashbia ani aleichem im lo tavo'u u'sa'idu li" - "I impose an oath upon you if you will not come and testify for me" - and he asks them to testify about one of the following matters:
"She'ani kohen" - that I am a kohen, or "she'ani Levi" - that I am a Levi: testimony about his lineage.
"She'eini ben gerushah" - that I am not the son of a divorcee, for if he were the son of a divorcee he would not be fit for the priesthood.
"She'eini ben chalutzah" - that I am not the son of a chalutzah, for a chalutzah is forbidden to a kohen at least by rabbinic law, and her son is disqualified from the priesthood.
The reason the oath of testimony does not apply in these cases is that there is no monetary claim here, and the oath of testimony applies only to a monetary claim. This law is derived through a gezeirah shavah from the oath concerning a deposit, which too was stated with regard to a monetary claim.
A claim concerning a third party:
The mishnah continues: the claimant demands that the witnesses testify about another person - that so-and-so is a kohen or a Levi, or that he is not the son of a divorcee and not the son of a chalutzah. In these cases there are two deficiencies: besides the fact that they involve no monetary claim, they also do not come from the mouth of the claimant himself, but rather concern a third party. And it is a rule that the oath of testimony must come from the mouth of the claimant, from the person who is making the monetary claim.
The power of an authorization:
Indeed, even when the claim does not come from the mouth of the claimant, there are cases in which a third party can demand an oath of testimony - when he holds an authorization, a power of agency similar to a power of attorney. By virtue of this he may demand of someone, in the name of another person, that he come and testify. But this too applies only to a monetary claim, and in the cases before us, even if he held an authorization, the oath of testimony would not apply, since there is no monetary claim here.
Rape and seduction - when the authorization is of no help:
The mishnah continues with a case involving a third party: someone raped another man's daughter and became liable for payment, or he seduced her and became liable for payment. In both of these cases, even though this is a monetary claim, and even if he came with an authorization, the authorization is of no help. For an authorization is effective only with regard to money that originally belonged to the claimant: a person who left a deposit with his fellow or lent him money is claiming back his own money, and in such a case the power of agency is effective. But in cases of damages that money was never in his possession, and this is nothing but a claim for compensation, and for compensation an authorization is of no help. Therefore, even though this is a monetary claim, the oath does not take effect: the oath of testimony applies only when it comes from the mouth of the claimant himself or from someone who holds the power of an authorization, and here the authorization is of no help.
Cases that carry liability for the death penalty:
The Mishnah continues and lists three additional cases:
"V'shechaval bi b'ni" - that his son wounded him, an act that carries the death penalty.
"V'shechaval bi chaveri" - that his fellow injured him and drew blood from him on Shabbos.
"V'shehidlik li g'dishi" - that he set fire to his stack of grain on Shabbos.
"Harei eilu p'turim" - they are exempt from the oath of testimony, because there is no monetary obligation here. And why is there no monetary claim? Because since these acts carry the death penalty, we apply the principle of "kim leih bidraba mineih": since he is liable to death, or performed an act that could bring him to the death penalty, the monetary responsibility falls away from him. And since there is no monetary claim, the oath of testimony does not apply.
In summary: In this Mishnah we learned three grounds for exemption from the oath of testimony: testimony that carries no monetary claim with it (such as testimony about lineage of kehunah or leviyah); testimony that does not come at the demand of the claimant himself but concerns a third party, where even a power of attorney does not help when the claim is one of damages and compensation rather than money that was originally in his possession; and cases that involve the death penalty, where the liable party is exempt from the monetary payment by force of the principle "kim leih bidraba mineih".