Technically, "A Rose for Emily" is written in the first person, but it can be easy to be confused on this subject. The perspective of the story is not a common one. It is certainly not an omniscient perspective—we know this because the reader does not know anything more than the narrator knows, either about what is going on in Miss Emily's house, what happened to Homer Barron, or anything else. An omniscient narrator is one who stands outside of the story and knows everything that is going on in the minds of all the characters in the story. In the case of this story, the tension and suspense are greatly heightened by the fact that we do not know what Emily is thinking or feeling, or what is going on inside the house. Instead, we, like the narrator, are in the same position as everyone else in the town, watching from afar.
A first person narrative usually uses "I" rather than "he" and "she." In this story, the first person narrator is part of a collective: "our town." He does not identify himself specifically, but uses "we" phrases to give a sense of what the town was feeling and thinking as events wore on. This narrative allows for sentences like:
So THE NEXT day we all said, "She will kill herself"; and we said it would be the best thing.
The style is almost that of town gossip, and seeing through the eyes of these watching townspeople, we become as involved as they are in the strange events at Miss Emily's home.