For those who aren't familiar with the story, here's a quick summary: Connie is a fifteen year old who is interested in her looks and boys and hanging out. One day, while alone at the house, Arnold pulls into her driveway and tries to get her to leave with him. She's seen him one before and thought he was about her age. It becomes increasingly clear that Arnold is not who he seems to be at first glance.
Here's the first line of the story:
Her name was Connie. She was fifteen and she had a quick, nervous giggling habit of craning her neck to glance into mirrors or checking other people's faces to make sure her own was all right.
Ok, we're all caught up. On to the question. Who is the narrator? Let's start by looking at who isn't the narrator. Connie's mother isn't the narrator. If she were, the story would be in first person and the reader wouldn't have access to anything the mother didn't witness, such as Connie's exchange with Arnold while the rest of the family is away. And she wouldn't know—with certainty—Connie's inner thoughts, which we see often in the story.
Some we might say the author is the narrator, but that's not a good way to think about the third person narrator. Though the author is, ultimately, the one writing the story, the sentiments and voice of the third person narrator aren't necessarily the same as the author's.
The last suggestion gets closer to the identity; the narrator is an entity hanging above the scene, relating it to the reader. However, this narrator is not omniscient. An omniscient narrator knows all, but this one has limitations. For instance, the narrator doesn't know what Arnold is thinking. That's part of the brilliance of this story; the reader makes discoveries about the true nature of Arnold's visit as Connie begins to do the same. In fact, the narrator seems to see things the way Connie does. Take these lines, for example:
Her sister June was twenty-four and still lived at home. She was a secretary in the high school Connie attended, and if that wasn't bad enough—with her in the same building—she was so plain and chunky and steady that Connie had to hear her praised all the time by her mother and her mother's sisters.
It's Connie who thinks June working at the school is “bad" and that June is “plain and chunky and steady." Their mother, who praises June, would probably think of her differently, perhaps as reliable and practical. And the story gets even more intimately invested in Connie's thoughts. Here, she thinks of the boy she met the night before:
. . . how nice he had been, how sweet it always was, not the way someone like June would suppose but sweet, gentle, the way it was in movies and promised in songs; and when she opened her eyes she hardly knew where she was, the back yard ran off into weeds and a fence-like line of trees and behind it the sky was perfectly blue and still.
Still, the narrator is not Connie. This would have to be in first person—using Connie's words—for that to be the case. But the third person narrator is somewhat close to Connie. The reader experiences the story through Connie's perspective.
So who is the narrator? It's not a specific person—a character or the author—but rather an unnamed entity with access to Connie's inner experience. When using third person, your job as the writer is to establish this unnamed entity's limitations.
In the end, perhaps answering the question of the narrator's identity is futile. The more focusing questions might be these: Which characters' thoughts can the narrator access? What makes the narrator's voice distinctive?