The US has a Common Law system so case law is as important as code (or even more so). The question isn't whether there's "a law", the question is whether there have been cases fought over it and what the outcome was. That seems harder to google.
Likewise I have yet to hear a coherent legal justification for the idea of the "state monopoly on violence" that doesn't boil down to a just-so story invoking the fiction of the social contract (even the US only grants a limited exemption to this via the second amendment and even that still uses the context of "militias"). But even in Civil Law systems that doesn't mean the state won't act as if it is a thing and base legislation on that assumption.
Likewise I have yet to hear a coherent legal justification for the idea of the "state monopoly on violence" that doesn't boil down to a just-so story invoking the fiction of the social contract (even the US only grants a limited exemption to this via the second amendment and even that still uses the context of "militias"). But even in Civil Law systems that doesn't mean the state won't act as if it is a thing and base legislation on that assumption.