Some local departments buy through their county improvement authority or another county consortium, which buys in larger quantities and gets better prices and/or allows better financing options. That leads to CG plates. I don't know for sure but would suspect the same for Franklin.
Yes, I've heard that Franklin PD gets their cars through the county purchasing agent. From what I understand, if the agency goes through the county for purchasing and/or financing, the vehicle will receive 'CG' plates.