We really do need to know what conductor you are talking about. Is this panelboard the building Service Entrance? Is it the Grounding Electrode Conductor at the SE or is it current flow on an Equipment Grounding Conductor that is part of a feeder to a remote panelboard?
Look at 250.6
If it is the GEC of the main disconnect/service panel, then the nature of the POCO MultiplyGroundedNeutral system that some current will flow in the GEC. This is because the path through your Ground Electrode to the POCO Ground Electrode at their transformer is electrically in parallel with their neutral.
If it is the EGC between a subpanel and the service disconnect, then current there would be an indication either of a ground fault downstream which would trip a GFI if one were present OR a downstream connection between the grounded equipment and local earth (such as water piping or a separate (unnecessary and potentially harmful) ground rod required by an equipment manufacturer. To check this out you can put an amp clamp around all of the ungrounded lines going to the subpanel and check whether or not you see the same current as when clamping the EGC.
