I wouldn't call this particular example a "crime," but in Chapter 9 of To Kill a Mockingbird, Scout comes downstairs from her Finch Landing bedroom for a drink of water and hears Atticus and her Uncle Jack talking. So, she deliberately eavesdrops on their conversation. The two brothers are talking about Scout's earlier fight with her cousin, Francis, and Atticus is giving Jack advice on how to handle children. The conversation then shifts to talk of the upcoming Tom Robinson trial. Atticus tells Jack that he took the case because he couldn't "face my children otherwise... I just hope Jem and Scout come to me for their answers instead of listening to the town. I just hope they trust me enough..." At this point, Atticus ends the conversation and calls out "Jean Louise?... Go to bed." Atticus knew she had been listening the entire time, but he wanted her to hear the conversation in the hope that she would trust him enough to honor his decisions regarding his children. Scout "scurried to my room... and it was not until many years later that I realized he wanted me to hear every word he said."
Atticus knows of Scout's "crime" of being able to read.
On her first day of school, the new teacher, Miss Caroline Fisher, calls on Scout to read the enormous square capital letters that she has printed on the blackboard. As Scout recites these letters, Miss Caroline discovers that she is literate and "looked at [her] with more than faint distaste." She informs Scout that she must tell her father not to teach her any more because "it would interfere with my reading."
Surprised by her teacher's disparagement of her father, Scout returns, "Teach me? ... He hasn't taught me anything, Miss Caroline." She goes on to explain that Atticus is so exhausted in the evenings that he simply retires to the living room, where he reads. But Miss Caroline asks her who did teach her if not her father; then, she instructs Scout to inform her father that he must not teach her to read as it is best to begin with a fresh mind. "You tell him I'll take over from here." She adds that her father does not know how to teach and instructs Scout to sit down.
I mumbled that I was sorry and retired meditating upon my crime. I had been wallowing illicitly in the daily papers. (Ch.2)
That evening Scout asks her father if she can stay home and be educated there just as he was educated at home when he was a boy. But Atticus replies that he has no time to be her teacher; he must make a living. Then, he explains to Scout that she must try to see things from the perspective of others. As a stranger to Maycomb, Miss Caroline must learn some things about "Maycomb's ways," and they must try to understand that she cannot be expected to understand everything right away. He knows, of course, that Scout has done nothing wrong in learning to read.
Discerning that Scout is really troubled that she has been told to no longer read at home with him, Atticus asks her if she knows what a compromise is, suggesting that if Scout will agree to go to school, they can continue reading together. But they should not mention their compromise at school because it could cause trouble with Miss Caroline. Scout agrees.