Your question refers to Atticus's mixed emotions about the Alabama death penalty in Chapter 23 of TKAM. After Jem complains about Tom's rape conviction, a capital offense in Alabama, Atticus "dropped his newspaper beside his chair" and had a man-to-man conversation with his son. Atticus "didn't have any quarrel with the rape statute, none whatsoever": Instead, it is the idea of a man facing the electric chair due to a conviction based entirely upon circumstantial evidence that bothers Atticus.
"--I mean, before a man is sentenced to death for murder, say, there should be one or two eye-witnesses. Someone should be able to say, ' Yes, I was there and saw him pull the trigger.' " (Chapter 23)
Atticus knows that without an eyewitness there will always be "reasonable doubt," but he believes that the accused deserves more than that: He calls for a "shadow of a doubt" when a man's life is at stake. Atticus also believes that a judge, not a jury, should hand down the death sentence.
In Chapter 23, Atticus discusses various aspects of the Tom Robinson trial with his children. When Scout asks what will happen to Tom Robinson, Atticus tells her that he will go to the electric chair if he loses his appeal. Jem then mentions to his father that he doesn't think Tom Robinson should die, even if he was guilty of assaulting and raping Mayella. When Atticus mentions that rape is a capital offense in Alabama, Jem argues that the jury could have given Tom twenty years instead of killing him. Atticus then points out that on a charge as serious as rape, the jury was either going to acquit or give Tom the death penalty. When Jem responds by saying that he doesn't think rape should be a capital offense, Atticus says that he has no quarrel with the rape statute. However, Atticus does have a problem when the jury gives the death penalty based on purely circumstantial evidence. Atticus believes that there should be at least one or two witnesses in order to give a man the death penalty. He also says that a defendant is entitled to a shadow of a doubt.