Let us remember that the tone is the attitude that the writer or speaker takes towards the characters and action in the story. If we examine the role of the narrator in this excellent short story, we can see that at various points he shows pity, horror, admiration and curiosity concerning Miss Emily and her life as he relates to us the incidents that make up her life and its chilling conclusion. However, I would argue that above all he, like the rest of the townsfolk, remains detached as Miss Emily is treated as something of an object of curiosity that is being looked at. Consider the way that this impression is presented in the opening paragraph of this story:
When Miss Emily Grierson died, our whole town went to her funeral: the men through a sort of respectful affection for a fallen monument, the women mostly out of curiosity to see the inside of her house, which no one save an old manservant--a combined gardener and cook--had seen in at least ten years.
From the very start of Miss Emily's story to her death (which comes at the beginning of this tale), both the narrator and the rest of the townsfolk remain detached and uninvolved in her story, even when it is clear that she is suffering under the "care" of her tyrannical father. Therefore we can describe the overarching tone of this work of fiction as being profoundly detached.