How to test hot tub grounding

I tried taking a multimeter to test for continuity between the house's ground and the hot tub water, but it didn't show anything.

You should not see anything if the ground were properly connected. Most of the time, the hot tub is fiberglass and the piping is plastic, so there should be no connection to ground, EXCEPT via the pump housing, assuming a metal volute (the chamber part of the pump) and a proper grounding conductor on that pump housing. So showing no voltage between ground and the water means they are are the same potential, which is what you want.

If I test for voltage between a phase and the hot tub water, I get 240V.

As you should in your system, because the neutral of your 240V TT system is connected to ground somewhere and so is your water (again, through the pump volute and the pump body being properly grounded), so measuring between those two points should show as the full 240V.

If I test for voltage between a phase and the hot tub water, I get 240V.

I'm a bit concerned about that. The big question is how much current is flowing during the test. If it is > 10mA then it should trip your GFCI, as you are leaking current through the hot tub water, which is exactly the hazard that a GFCI is supposed to prevent.

Is there anything else on this GFCI-protected circuit? If the GFCI circuit goes to a subpanel and there is a convenience outlet there then you can test it with a GFCI tester. If not, a little more work may be involved. It also seems odd that The hot tub is underground and its electrical panel is not easily accessible. See if you can trace where the wires go from the circuit breaker to the hot tub. There should be a relatively accessible junction box at the hot tub, even if the wires are coming through an underground conduit. Essentially you want to place a small load between a hot wire and ground that will draw a little more than 10mA. 240V x 10mA = 2.4W. So, in theory, any load > 3W to ground should trip the GFCI. Be very careful doing this, as a problem (fumbling with the wires) combined with the GFCI not working properly, could result in a very shocking experience.

If you're in North America or Japan, I am very concerned about this 240V reading between a phase and the hot tub water.

It's possible that your grounding is messed up, and your house is accidentally grounding to a phase. Generally, that happens with a combination of two things:

• A lost grounding electrode, so the system voltage ends up "floating" relative to ground.
• A hot-ground fault somewhere, which is biasing the system so one leg is now near ground, instead of netural being near ground as intended.
• You are then reading 240V from the other leg to ground.

So I would give your grounding electrode system a very thorough once-over, to make sure everything is in order. Don't be surprised if fixing the ground causes a circuit to malfunction; that would be the aforementioned hot-ground fault. Even though it seems like fixing ground broke the circuit, the circuit was already broken and you just improved the fault detection.

With that in good order, I would expect to measure 120V between either pole and the electrical wired ground at its location, and anything else associated with the hot tub.

Hot tub wiring is not to be trifled with - it can kill.