Although the first-person narrator in "The Tell-Tale Heart" by Edgar Allan Poe gives us a great deal of information about feelings and interior psychological states, we actually know very little about the external circumstances of the narrator's life, beyond the fact that the narrator lives in the same building as the old man.
Because the narrator writes in the first person, using the pronoun "I", there are no gendered pronouns referring to the narrator in the story, and no actual details revealing the gender of the narrator. Although most critics refer to the narrator as male, that is more evidence of male being the "unmarked" gender in our society than something based on clear textual evidence.
There are two possible hints that the narrator is male. The first is that in claiming not to be insane, the narrator sets up a contrasting image of "madmen" or "a madman"; were the narrator a female, she might have used the term "a madwoman." Secondly, the way the narrator moves furniture indicates some physical strength and the ability to move heavy objects unencumbered by the long, bulky skirts won by most women in the period. Neither of these two points are conclusive.
We do have a sense that the narrator, whatever the gender, is not only unreliable but insane. We have no information concerning the narrator's appearance, job, age, parentage, or any other such mundane details. By omitting such details, Poe focuses the readers attention on the psychological portrait of the narrator's disintegrating mind.