" The burden will now go to the people of Connecticut state to prove that you were driving over the speed limit."
This is wrong advice. The judge will always listen and believe the cop unless you have a solid proof. The burden of proof is yours, not the cop's.
I agree with Dindukhi, if you can afford it, lawyer up. Even when the Lawyer says the same thing that you are claiming, because of their position and possible rapport with the judge, the outcome could be different-on your favor.