The department said Tuesday the investigation is separate from a disciplinary investigation into Division of Criminal Investigation Special Agent in Charge Larry Hedlund, who was also involved in the April 26 incident.
The department's statement didn't identify the troopers. But Lt. Rob Hansen, a spokesman, has previously identified those involved as Steve Lawrence, who was driving the governor; and Matthew Eimers, who clocked the governor's SUV at 84 mph but didn't pull it over.
Lawrence and Eimers haven't returned messages seeking comment.
The department says it'll release more information after the two investigations are completed.