Rambam, Hilchos Eidus, Chapter 5: 

Chapter 5: The testimony of a single witness, and a witness serving as a judge

Halacha 1: The testimony of a lone witness

• It’s invalidity for giving a verdict: The testimony of a lone witness is not acceptable in court to use for the giving of a verdict.
• This applies both by monetary cases and cases of capital punishment.
• It’s validity of forcing an oath: Nonetheless, the testimony of a lone witness is acceptable to force an oath on the other party.

Halacha 2: Cases in which testimony of a lone witness is acceptable

• There are two cases in which the Torah accepted the testimony of a lone witness.
  • A Sotah.
  • Egla Arufa
• The law by a Sotah: The Torah believed a lone witness in the case of a Sotah to prevent her from drinking the bitter waters if he testifies to adultery.
• The law by Egla Arufa: The Torah believed a lone witness in the case of a Egla Arufa to prevent the calf from being killed if he testifies to have seen the murderer.
• Testimony of death of a woman’s husband: The rabbis accepted the testimony of a lone witness who claims that a woman’s husband has died, in order to permit her to remarry.

Halacha 3: Accepting an invalid witness as a lone witness

• In all cases that the testimony of a single witness is accepted, the testimony of a woman or other invalid witness is acceptable.
• Forcing an oath: The one exception to this rule is by an oath, that we do not force an oath due to the testimony of a single witness unless he is a valid witness.

Halacha 4: If an invalid witness is found amongst a group of witnesses

• If an invalid witness is found amongst a group of witnesses who came to testify, such as if one of the witnesses is a relative or has another invalidation, than the entire group of witnesses is deemed invalid.
• This applies both by monetary cases and cases of capital punishment.
• If they did not come to testify: This, however, only applies if they all intended to testify. If, however, the group of witnesses who came to testify does not contain an invalid witness, even though invalid witnesses, such as two brothers, were also eyewitness of the event, then their testimony is accepted.

Halacha 5: Excluding the invalid witness from the group

• It is possible to exclude invalid witnesses from a group of witnesses in the following manner: The court asks the group of witnesses as to which witnesses saw the event for the sake of testifying regarding it, and which simply happened to be there and saw it. They then separate the two groups of people, and if within the group of those who stated that they intended to testify there are no invalid witnesses, then their group is validated even though the other group contains invalid witnesses.
• If both groups contain valid witnesses, that they are all considered one group and all their testimony is accepted.

Halacha 6: If an invalid witness is found on a document with a number of signatures

• If an invalid witness is found amongst the many signatures of witnesses on a document, then if there is testimony that they invalid witness was part of the intended group of witnesses then the document is invalid. If, however, no such testimony exists in the document is valid as we assume that the invalid witness signed on his own without being summoned to do so.

Halacha 7: If the first witness to sign was invalid

• Even if the first witness to sign of the document was found to be an invalid witness, nonetheless we accept the document if there is no testimony that he was part of the original group of intended witnesses.

Halacha 8: A witness cannot become a judge in the case

• Capital punishment cases: A witness to an event involving a case of capital punishment is invalid to serve also as a judge regarding that case.
• Arguing for the guilt or innocence of the defendant: It is forbidden for him to argue on behalf of the case either for innocence or guilt.
• Monetary cases: A witness to an event involving a monetary case is also invalid to serve as a judge regarding that case. Nonetheless, he may argue on behalf of the defendant either for guilt or innocence.

Halacha 9: The law by cases in which testimony is not required

• The above invalidation for a witness to serve as a judge in the tribunal only applies in scenarios in which witnesses are biblically required to establish the verdict. However, in those cases that testimonies is only Rabbinically required, then a witness can also serve as a judge of the tribunal.
• For example, a person who brought a Get from overseas may testify that it was written and signed before him and then go ahead and serve on the tribunal which then gives the Get to the wife.