Where do references to the Civil War occur in the story? How does the war play a part in the story?
The story "A Rose for Emily" and the title character Emily Grierson show the world of the South as it experienced a fundamental shift, from the days of slavery and aristocratic plantation owner families (of which the Griersons are one) that is coming to an end when Emily is born to the new, post-Civil War world, where antebellum chivalry is lost to the push for progress. The war comes up, explicitly and implicitly, when these conflicts between old and new and tradition and progress come to the surface.
Emily Grierson experiences the changes that the Civil War and its outcome makes on the South and her hometown of Jefferson. Cast as an aging Southern belle domineered by a controlling father, Emily has few chances to break the mold of tradition, and she doesn't until her affair with Homer Barron in her thirties. When that fails to lead to the appropriate marriage and fulfillment of her traditional role, she clings to the other antebellum option for unmarried ladies: that of a haughty, mysterious spinster.
It is note-worthy that when Emily chooses to follow her own heart and pursue a man sexually, she chooses Homer Barron. First, he is a Northerner, and so emblematic of the changes caused by the war. Second, he's in town for a sidewalk construction project, making him an example of the sweeping changes of the North coming in to change the nature of the South. That Emily chooses him suggests an even deeper rebellion against the traditional Southern ways and ties in to the conflicts set up by the Civil War.
Another way the war sets up a conflict between the old ways and new is in the townspeople's interactions with Emily. Men like Colonel Sartoris and Judge Stevens still subscribe to Southern chivalry and they see Emily as a damsel in distress, a woman who must be protected, and so they remit her taxes and refuse to confront her about the smell coming from her house, respectively. As time goes on, however, and the post-war changes continue, new aldermen, who don't follow the same rules of chivalry, come to try to collect Miss Emily's taxes. This event shows the conflict of the new South, where progress is king, and the old.