D

To determine why no current flows between two connected charged bodies, we need to analyze the conditions under which charge movement occurs.
Step 1: Understand that electrical current flows due to a potential difference (voltage) between two points. When two charged bodies are connected, the potential difference drives current flow.
Step 2: Charge is distributed among the two bodies, and if they have the same potential, no net movement of charge occurs, meaning no current flows.
Step 3: Thus, the correct conclusion is that current will not flow when the two bodies have the same potential ratio.
In summary, if the potentials are equal, the electric field between the bodies is zero, leading to no movement of charge and hence no current. Therefore, option D is correct.