I'm not sure it really fits the bill there. It had a largely-ceremonial hereditary monarchy (which Pippin inherits from his dad about 15 years after the ring was destroyed) which can call assemblies to discuss matters, an elected mayor (which Sam served as several times over after the ring), and law enforcement in the form of the shiriffs. Tolkien does describe it as "hardly any" government, yes, but to me it seems perhaps unsurprisingly more like a miniaturised version of the British system
I mean, medieval communities were often somewhat self-managed due to the simple fact that judicial courts were far away, and the local bailiff had to enact the laws. Every-day law was mostly on a by-case basis, and if they didn't notice or care, there was no law.