Explain, please.
There is no solid direct - or even indirect - physical evidence. Only a great amount of circumstantial evidence. It sure looks like he did it. But in other cases it has looked that way also and the state turned out to be wrong.
Not looking at this specific case, but on the principal that civil liberties must be protected above other desires and considerations - in this case, wanting to put Peterson to death for the horrible crime most people think he committed.