Also from the hunting and trapping guide:
License Suspensions Remedial Hunter Ed Requirement
In accordance with Connecticut General Statute 26-61, payment of a fine, forfeiture of a bond or a plea or judgement of guilty for a fishing, hunting, or trapping violation will automatically result in the suspension of all fishing, hunting and trapping privileges including your fishing, hunting and trapping license.

Key point being, payment of a fine or guilty judgement by statute results in suspension of license. I couldn't find anything about for how long, perhaps D.E.P decides that.