Sounds like a NEUTRAL - GROUND issue.
NOTE WELL: they are not the same thing.
That said if you still have a measurable voltage when the building main (not simply the apartment)is disconnected from the source it has to be something else.
I have heard but never seen, that junk metal buried in the earth can produce a slight electric shock under some conditions.
Are the water supply lines nonmetallic?
Typically with copper or galvanized pipe, the faucet would be grounded. Not so with PEX or some others.
Also, the supply tubes from the stop(valve) to the faucet are often plastic.
If you run a wire from the faucet to a known ground does it still show voltage on a meter? Any sparks when grounding the faucet?
Guessing that it is a stray voltage from a poor ground or ground connection.
In some locations, the local power company will look at the problem.
The building is a townhouse, 4 stories, a basement apt. with the problem and 3 floors upstairs. I know the voltage was there when we turned off the apartment main. The apartment gets one electric bill, the upstairs a different metered bill. We did not try turning off both mains. We will try that. I have never seen a spark, and I can’t feel the voltage (5v). The house was built in 1901, so metal, not plastic pipes from street. I looked where the water cut-off is, the pipes appeared to be galvanized not copper, and a wire aimed in the direction of the electric panel passing behind the drywall seemed firmly clipped to the water pipe. Any other ideas?? Anyway, thanks.