The "Boo Radley" game begins in chapter 4 of To Kill a Mockingbird. The game involves the children playing various roles, with the part of Boo Radley belonging to Jem. Their drama is "woven from bits and scraps of gossip and neighborhood legend."
Scout wants to quit the game for two reasons. One day, Atticus happens to see the children playing the game. Atticus asks, "Does this have anything to do with the Radleys?" Jem denies that it does. This is the first reason Scout wants to quit the game. She doesn't want to be in trouble with Atticus.
The second reason Scout wants to quit the game involves a previous incident. Earlier, when Scout, Jem, and Dill are playing outside, Jem rolls Scout in a tire. She lands in the Radley's front yard after bumping into the steps of their porch. She doesn't share this information with the others, but when she falls out of the tire, she believes that "Someone was inside the house laughing." This is her second reason she thinks it would be best to stop playing the "Boo Radley" game. She is fairly certain that Boo must have seen them.