Not to put an innocent person to death on the basis of circumstantial evidence

That He prohibited the judge to declare punishments by way of strong conjectures, and even when it is almost certain. For example, that one man is running after his enemy to kill him; and in order to escape from him, he enters a house; but then the pursuer runs behind him. And others enter after him and find the pursued in death throes, while his enemy that was pursuing him is standing over him, the knife dripping blood in the hand - the [court] may not kill him, from the angle of executing the punishment, since witnesses are not testifying that they saw the killing. And the prohibition about killing this one comes in the Torah; and that is His saying, "do not kill an innocent righteous man" (Exodus 23:7). And in the Mekhilta (Mekhilta d'Rabbi Yishmael 23:7:2), they said, "If they saw him pursuing another to kill him, and they warned him and said to him, 'He is an Israelite, he is a Son of the Covenant; and if you kill him, you shall be killed.' But they averted their eyes, and found [the one pursued] in the death throes, the knife dripping blood in the hand of the murderer - I might understand that he is liable [for the death penalty. Hence] we learn to say, 'do not kill an innocent righteous man.'" And do not dismiss this and wonder about this law. For among possible things, there are things that are very likely, things very unlikely and things in between; so that there is a wide spectrum of what is possible. And if the Torah had permitted declaring capital punishments in very probable cases - when it is very close to actuality, like the case of our example - we would declare the punishment in that which is a little removed from this, and [eventually] also in that which is far removed. Until they would declare the punishments and kill people with a weak conjecture, according to the imagination of the judge and his thought. Therefore He, may He be exalted, closed this opening and said that he not declare the punishment until witnesses testify that they know with certainty that this one did the act - without a doubt and without any guesswork at all. And when we do not declare punishments based on strong appearances, the end result is surely that we will acquit the sinner. But if we declare punishments based on appearances and conjecture, we would surely sometimes kill someone innocent. And likewise when two witnesses testify to two sins, each of which has a death penalty. For example, one of the two saw him transgressing one [sin] alone, and the other saw him transgressing the other - behold, this one is not killed. And the example about this is such as if one testifies that he did work on Shabbat and warned him; and the other testified that he worshipped idolatry and warned him - this one is not stoned. They, may their memory be blessed, said, "[If] one testified against him, 'He worshipped the sun,' and another testified against him, 'He worshipped the moon,' I might understand that they combine [to constitute the necessary two witnesses. Hence] we learn to say, 'do not kill an innocent righteous man.'" (See Parashat Mishpatim; Mishneh Torah, The Sanhedrin and the Penalties within their Jurisdiction 20.)