Dark Hollow, by Anna Katharine Green. Part VI.

Twelve years ago, the town of Shelby was in shock at the discovery of the murder of Algernon Etheridge, one of the town's most prominent citizens. His body was found beaten to death, and robbed, on the bridge in Dark Hollow. The local Innkeeper was quickly accused, tried and found guilty. He was sentenced to die in the electric chair by Judge Ostrander, who was the victim's best friend.

Then one day, a woman shows up, dressed all in purple and acting very mysterious. Her goal, it turns out, is to get the Judge to acquit the killer. But what is the purpose? The killer is dead. No one can change that. She begins looking for circumstantial evidence the trial used for the conviction, and obtains a job in the Judge's house as his housekeeper. She is determined to clear the killer's name, no matter the cost.