Objection 1. It would seem that a man is not bound to give evidence. Augustine say (QQ. Genesis 1:26) [Cf. Contra Faust. xxii, 33,34, that when Abraham said of his wife (Genesis 20:2), "She is my sister," he wished the truth to be concealed and not a lie be told. Now, by hiding the truth a man abstains from giving evidence. Therefore a man is not bound to give evidence.
Objection 2. Further, no man is bound to act deceitfully. Now it is written (Proverbs 11:13): "He that walketh deceitfully revealeth secrets, but he that is faithful concealeth the thing committed to him by his friend." Therefore a man is not always bound to give evidence, especially on matters committed to him as a secret by a friend.
Objection 3. Further, clerics and priests, more than others, are bound to those things that are necessary for salvation. Yet clerics and priests are forbidden to give evidence when a man is on trial for his life. Therefore it is not necessary for salvation to give evidence.
On the contrary, Augustine [Can. Quisquis, caus. xi, qu. 3, cap. Falsidicus; cf. Isidore, Sentent. iii, 55 says: "Both he who conceals the truth and he who tells a lie are guilty, the former because he is unwilling to do good, the latter because he desires to hurt."
I answer that, We must make a distinction in the matter of giving evidence: because sometimes a certain man's evidence is necessary, and sometimes not. If the necessary evidence is that of a man subject to a superior whom, in matters pertaining to justice, he is bound to obey, without doubt he is bound to give evidence on those points which are required of him in accordance with the order of justice, for instance on manifest things or when ill-report has preceded. If however he is required to give evidence on other points, for instance secret matters, and those of which no ill-report has preceded, he is not bound to give evidence. On the other hand, if his evidence be required by authority of a superior whom he is bound to obey, we must make a distinction: because if his evidence is required in order to deliver a man from an unjust death or any other penalty, or from false defamation, or some loss, in such cases he is bound to give evidence. Even if his evidence is not demanded, he is bound to do what he can to declare the truth to someone who may profit thereby. For it is written (Psalm 81:4): "Rescue the poor, and deliver the needy from the hand of the sinner"; and (Proverbs 24:11): "Deliver them that are led to death"; and (Romans 1:32): "They are worthy of death, not only they that do them, but they also that consent to them that do them," on which words a gloss says: "To be silent when one can disprove is to consent." On matters pertaining to a man's condemnation, one is not bound to give evidence, except when one is constrained by a superior in accordance with the order of justice; since if the truth of such a matter be concealed, no particular injury is inflicted on anyone. Or, if some danger threatens the accuser, it matters not since he risked the danger of his own accord: whereas it is different with the accused, who incurs the danger against his will.
Reply to Objection 1. Augustine is speaking of concealment of the truth in a case when a man is not compelled by his superior's authority to declare the truth, and when such concealment is not specially injurious to any person.
Reply to Objection 2. A man should by no means give evidence on matters secretly committed to him in confession, because he knows such things, not as man but as God's minister: and the sacrament is more binding than any human precept. But as regards matters committed to man in some other way under secrecy, we must make a distinction. Sometimes they are of such a nature that one is bound to make them known as soon as they come to our knowledge, for instance if they conduce to the spiritual or corporal corruption of the community, or to some grave personal injury, in short any like matter that a man is bound to make known either by giving evidence or by denouncing it. Against such a duty a man cannot be obliged to act on the plea that the matter is committed to him under secrecy, for he would break the faith he owes to another. On the other hand sometimes they are such as one is not bound to make known, so that one may be under obligation not to do so on account of their being committed to one under secrecy. On such a case one is by no means bound to make them known, even if the superior should command; because to keep faith is of natural right, and a man cannot be commanded to do what is contrary to natural right.
Reply to Objection 3. It is unbecoming for ministers of the altar to slay a man or to cooperate in his slaying, as stated above (Question 64, Article 4); hence according to the order of justice they cannot be compelled to give evidence when a man is on trial for his life.
Source: Summa Theologica (New Advent)