I'm not sure this is really a question for a lawyer. The person you were convicted of killing is alive, a crime hasn't been committed, here or by the sounds of it in your own world. So I'm not really sure what you'd tell law enforcement.
Pressing criminal charges is part of what my office does here, and I can't see a case to be made here so unless you think you're likely to go through with the act you were accused of and need the local police force to keep an eye on you, I don't know what you'd gain from telling anyone. Other than perhaps a kind of wariness that can make settling in a new place all the more difficult.