Sanhedrin 33A

מיכן שפותחין בדיני נפשות תחלה לזכות.

From here it is derived that in cases of capital law, the court opens the deliberations by first raising a claim to acquit the accused. This baraita corresponds to the explanation of Abaya and Rava that the court notifies the accused that he has nothing to fear if he is innocent.

דיני ממונות מחזירין כו׳. ורמינהו: דן את הדין, זיכה את החייב, חייב את הזכאי, טימא את הטהור, טיהר את הטמא ⁠– מה שעשה עשוי, וישלם מביתו.

§ The Mishnah teaches that in cases of monetary law, the court brings the accused back to be judged again if new evidence arises, whether with a claim to exempt him or with a claim to find him liable. In cases of capital law, the court brings the accused back to be judged again with a claim to acquit him, but does not bring him back to be judged with a claim to find him liable. And the Talmud raises a contradiction from a Mishnah (Bekhorot 28b): If a judge issued a judgment and erred, so that he exempts a liable party or finds an innocent party liable, or if he ruled that a pure item is impure or ruled that an impure item is pure, and by doing so he caused a litigant a monetary loss; what he did is done, i.e., the judgment stands, and the judge must pay damages from his home, i.e., from his personal funds. This indicates that the court does not bring the accused back to be judged again if new evidence arises.

אמר רב יוסף: לא קשיא, כאן במומחה, כאן בשאינו מומחה. ובמומחה מחזירין? והקתני: אם היה מומחה לבית דין ⁠– פטור מלשלם!

Rav Yosef says: This is not difficult. The Mishnah here, which teaches that the court does bring the accused back to be judged again if new evidence arises, is stated with regard to a judge who was an expert, whereas the Mishnah there in tractate Bekhorot, which teaches that what he did is done, is stated with regard to a judge who was not an expert. The Talmud asks: And does one bring the accused back in the case of a judge who was an expert? But that Mishnah in tractate Bekhorot teaches: If he was an expert accepted by the court he is exempt from liability to pay. This indicates that the court does not bring the accused back to be judged again if new evidence arises, even if the judge is an expert; otherwise there would be no need to state that the judge is exempt from liability to pay.