When subpoenas can be issued, by who, and when, varies from state to state (and in the federal world, agency to agency). There are definitely administrative subpoenas, investigatory subpoenas, etc, depending on who and where.

Back in 2000 (best data i can find on short notice), at least 12 states permitted prosecutors to serve investigative subpoenas on targets, witnesses, and record keepers before they charge a person with a crime

Where the state wants to, it can press charges on its own. It's up to the prosecutors, generally. This is why there are cases like "so and so vs. New Jersey". In cases like murder and such, the state is the only viable prosecutor, which is why the prosecutor works for the state.

That said, I don't know the procedure for determining whether or not an actual crime has been committed, and without there being an actual case in hand, I have no idea if the subpoenas are valid.