In short:
Luigi Mangione has pleaded not guilty to state murder and terror charges.
Mr Mangione is accused of killing UnitedHealthcare CEO Brian Thompson outside a Manhattan hotel.
What’s next?
Prosecutors say the state case is expected to run parallel to a federal prosecution.
Ah.
It seems like the court system you describe is considered an investigative body.
Under the US system, the investigation proceeds independent of the courts. The fall guy pleading guilty doesn’t stop the investigation.