Well you set yourself up a motive to get charged with 1st, and even 1st degree murder, the murderer could call the cops on themselves. You may even get a voluntary manslaughter in the first act, since the death was maybe accidental, if you acted without intent to kill.
But anyways, with the forensic science of today, chances are if you have to even ask what would you do, then you would get caught either way, so a smart, rational person takes the course of least punishment to themselves. If you run, hide, try to cover it up, steal his belongings, then when you do get caught, your punishment will be worse.
If you are a sociopath, then it doesn't matter what you do, because you wont care.