Juno said:
I'm sure if she killed someone she had a very good reason to do so.
Katholic Nun said:
The victim probably deserved it.
This seems to be the main issue that goes unaddressed in the original question: Is this murder in actuality or simply in the eyes of the law? That is, was this an unjust killing (murder), or was the situation not so morally black-and-white? Did the best friend shoot a child molester in self-defense in the heat of the moment, or did the best friend hang an old lady who looked at him funny after planning the deed beforehand? More importantly, does this change your answer?
If we are in fact talking about an unjust killing here, my course of action would be first to try to convince my best friend to turn himself in because it's the right thing to do. If my friend goes two days without doing so or I learn he's killed someone else, I turn him in myself. I would only tell my friend I might turn him in if I don't deem him to be a danger to myself.
I have two lines of thinking for my answer, one secular and one spiritual.
Thinking secularly, friendship is not unconditional. I would never be best friends with someone if I thought they would ever murder someone. I might still try to be some kind of friend to them in the hopes I can dissuade them from killing someone, but I would always think of them as more of a danger to handle than a true friend. If it turned out I was so drastically wrong about someone's moral compass, I would hope they'd immediately lose my best-friendship, no matter how much it hurt. At that point he's a murderer, not my best friend, and I would fulfill my obligation to society to see that he ends up in the hands of the law.
Thinking spiritually, if I believe that someone has knowingly killed someone unjustly, then I believe that they've opted for eternal misery after they die. Morally, my obligation is to get them to repent and seek salvation from this. I don't believe that there is repentance for murder without making reparations, and part of this must be subjecting oneself to the mercy of society, because one's right to be a normal member of society is forfeited when one commits murder. Moreover, I don't see how one can repent from murder while enjoying the freedom of having gotten away with it; it's like seeking forgiveness for robbery while you intend to keep all the money.
If, however, the killing wasn't murder and I don't see my friend as a threat to those around him and I don't think he's going to Hell for it, I don't know what I'd do.