Yes, they would in some instances. Think about the cases where a non-inebriated driver kills someone in a car accident. Usually nothing would be done, but if they could prove somehow that the action was somehow intentional or reckless, or other unusual circumstances then yes, they would be charged with involuntary manslaughter.
Actually given the case in this story, Superman could actually be charged with voluntary manslaughter and dare I say some type of lower murder charge (The different types are called different things in different states. For example - some states call a planned murder premeditated while other would say first degree murder.)
