The "crime" that the narrator refers to in Chopin's "The Story of an Hour" relates to the unwritten rules in the institution of marriage at the time of the story. Louise has just learned that her husband Brently is dead, so she ponders the life that she has had with him compared to the life that she thinks she will have in the future without him. She thinks: "There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature." Here, Louise suggests that her husband forced a lifestyle upon her that she did not want. She does not believe that her husband intended to make her unhappy or that he intentionally acted cruel; however, the imposition was still wrong: "A kind intention or a cruel intention made the act seem no less a crime as she looked upon it in that brief moment of illumination." So, the "crime" according to Louise is forcing someone to live a lifestyle that he or she does not want.
This is related to the theme of the story because the story overall is about the nature of freedom and its importance to the individual, in this case, particularly women. Louise is representative of married women in the late 19th and early 20th centuries who felt trapped in their marriages because they had no say in how their lives progressed. Chopin herself did not become a writer until her husband passed away. So, the story suggests that people do not have the right, even if married, to hinder the freedom of their partners.