About half of the legal systems in the world are called "Civil courts." They are wholly separate from the criminal courts run by the state's judicial branch.

Private law is just as common as state law in most countries. You may have used civil courts already without knowing you did so, such as if you bought real estate.

Cases with externalities like toxic dumping usually wind up in the criminal courts, but that really depends on if there was a pre-existing contract between the plaintiff & defendant.