So if your on city water and have not put any water in the tank, then it should be empty. The city water system is seperated from the tank system. I would suspect a leak in the city water system.
Try filling the tank and running off that ( you will need to have the pump on) for a little while. See if you still have that wet spot.
If the pump keeps running even when you are not using any water, you will know that you have a leak in a shared component and I would suspect the water heater or lines to the water heater are leaking.
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