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Potentially very dangerous. So no one should get into this tub until problems are solved.
However, I have questions.
1. Assume the tub is metal, conductive. The water piping is conductive and electrically connected to the metal tub, meaning a low resistance connection. Also assume the water is of some nominal conductivity. This whole combination of items --- tub, piping, and water --- is at an approximately equipotential within the water and the tub under the above conditions. The whole thing could be 1,000,000 volts above earth and it would not change what was in the tub. If the person in the tub does not touch anything outside the tub, then how do they get a shock?
2. This means you need to know if all the above said components are conductive and electrically connected together (bonded).
3. Assume they are all bonded together, then my assumption is that the shock occurs when getting into the tub, or when reaching for something outside of the tub, or someone puts an electrical current into the water in the tub.
Injecting current into the water in the pipe coming to the tub is unlikely to create a potential difference within the tub water and/or relative to the tub or faucet. Assuming the piping and attached faucet are conductive. Current in the water source coming into the tub would be shunted to the metal pipe and tub before creating a field in the tub.
4. In its present state put water into the tub. Get a high impedance digital voltmeter, like a Fluke 27. Run a test lead wire from some rod, maybe a 12" screwdriver, driven in the earth near the main service entrance. This test lead is one input to your meter. Use AC volts or millivolts range as required. With the other test lead measure the voltage to different things in this bath area --- water in tub, tub, faucet, water coming out of faucet, the floor, and anything that can be touched.
In one of my bathrooms I get 5 MV AC from the water stream to the outlet EGC. Less than this from the water stream to the faucet. Quite erratic and below 3 MV. Maybe varying DC generated from dissimilar materials.
When measuring to the tub itself there may be some problems because of the baked enamel.
If shocks really are occurring in the tub, then the above measurements may lead you in some particular direction.
Quite obviously the house, its electrical system, and the grid connections must be correctly connected for the ground and neutral.
My suggested measurements are a starting point. You can also put the meter in AC MA range and see what current levels you read.
It is important to find out what the exact conditions were when shocks occurred. At any time a minor shock could become much more serious because what ever current is causing the shock is being current limited by something. This current limiter might change and in turn cause a lethal shock.
I do not test myself or anyone for shock current levels. It is my understanding that something below 1 MA is where you feel a tingle. This might be 1/10 MA or even lower.
GFCI devices are supposed to trip on anything above 5 MA, but this gives you a substantial shock.
Also you should be careful running the tests.
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