What does the issue of confession in "The Tell-Tale Heart" tell us about the relationship between the individual and state authority?
Well, I don't know if it's possible for the narrator in this story to represent all individuals; the narrator is an "unreliable narrator" because he is clearly insane. Therefore, even his "confession" is suspect. Did it really happen as he said it did, or is this all in his mind?
Through his distorted lens, we might be describe his society as intrusive and alienating, though I certainly empathize with the neighbors! "A shriek had been heard by a neighbour during the night; suspicion of foul play had been aroused; information had been lodged at the police office, and they (the officers) had been deputed to search the premises." You might argue that it is alienating because rather than ask a neighbour what was wrong, they immediately launch a police investigation.
The police themelves are described entering the narrator's home with "perfect suavity" but they seem none too bright. It is the narrator's own fear and guilt that eventually does him in. (But again, is this confession the "truth" or the narrator's insane perception?)
As for the old man he kills, the narrator has all the authority, the older man all the (misplaced) trust. I suppose you could extend this analysis by looking at the imbalance of youth and age in Poe's time, or indeed in our own, arguing for the fear and loathing young people have of aging.