Re: What, no impeachment?
Is there even anything preventing the arrest of the POTUS in the theoretical case he actually provably murdered someone? Sure, you'd have to impeach him before he stops being the POTUS, but is there anything preventing his arrest?
Unsettled legal question, I believe. There has been some debate on whether POTUS can pardon him- or herself. You might think that a pardon would only apply after conviction (and thus after impeachment by the House and trial by the Senate), but presidents have issued pre-conviction and other sweeping pardons in the past, and thus far no one's tried to challenge them in the Supreme Court.
Arrest does not require conviction, but there's little point in trying to arrest a president who's been proactively pardoned for any applicable offense. Unless you want to roll the dice on SCOTUS overturning the pardon.
Combine that with the fact that the president controls the armed forces and is protected by the Secret Service, and that the vice president (who would promptly move into the Oval Office) is likely to side with the president, and my guess is that law enforcement officers would be reluctant to try it.
A POTUS who openly committed a serious crime and tried to remain in office could well precipitate a constitutional crisis. That scenario is not inconceivable, particularly at the present historical moment.
The US is still a relatively young country and there are more than a few corners of the law which have not been adequately explored.