How Much Is Normal

I agree that it sounds wrong to have the same current on the neutral lead and the ground lead. But it all depends on how you obtained these values, the actual values themselves and what current is the hot feed lines. Now if the neutral and ground current readings are both in the milliamp range, then I would not be alarmed. (You didn't tell us what current you found, you only said it was similar.) More likely, the wiring has been mixed up and some outlets have neutral and ground transposed somewhere. (I'd suspect this to happen in a building extension or in a hidden junction. Yeah, they're illegal but it does happen.)

Somewhere the neutral and earth conductors are touching and/or crossed over.

• Isolate the system from the mains supply.
• Using a multimeter set to ohms, disconnect each neutral wire from the common neutral bar at the dis-board one by one. Identify which circuit(s) has/have a neutral connected to earth.
• On the affected circuits only, work along them systematically downstream until each neutral-to-earth connection is found, and eliminate it/them.
• Once all the faults have been eliminated and all the neutral connections re-made at the neutral bar, re-energise the system.

If in doubt, consult a qualified electrician.

Which neutral? Are you referring to the neutral leaving the panel going back out to the utility transformer? If so, this does not make a lot of sense. Where did you measure the current in the grounding system?

If the neutral going out to the street shows no current, then the neutral back to the utility source is broken and the current is retuning on the grounding electrode conductor. Which is a common enough thing to happen in Canada. Our winters play havoc on our neutrals.

Or a neighbour on the same transformer has a broken neutral/ground system (and if the utility primary and secondary neutral is common to each other, he does not have to be on the same transformer for this to happen) and your grounding system is handling his return current. Also a common enough occurrence.

In any case, this is a dangerous condition. Call a licensed electrician as soon as possible.