Some US states still have private criminal prosecutions.

> Second, this Article demonstrates that the government monopoly on prosecution is an ideology rather than a rule. As it turns out, the government has never had total control over criminal law enforcement—not even exclusive authority to charge someone with a crime. While some courts prohibited private prosecution in the nineteenth century, others refused to abolish the practice. Public prosecutions of felonies and federal offenses became the norm in the progressive era, but private prosecution persisted in various forms. Particularly in “lowly” municipal courts, private individuals retained the ability to file and litigate criminal cases.

-- The Past and Persistence of Private Prosecution, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5210126