A voltmeter might pick up leakage, but to determine if it's hazardous, you need a load. I'd start with AC milliamp scale (try on high amp scale first, of course) to test further. It's probably a bad PSU just as you suspect (if you feel it it's maybe a few milliamps, but microamps might be acceptable). Connect one probe to ground, the other to the touchable metal part.
The 'correct' way to test involves a dive into a variety of national and international standards. One half milliamp into 1500 ohms parallel with
I'd expect that the output is nominally floating with respect to the AC input port. There usually are caps between line side and DC for EMI reasons.
I had a computer supply with a bad cap in the 5V standby supply. Caused the GFI to trip. Never did figure out the relationship between the cap and the symptom, but the cap fixed it.
When he mentioned "outer connector" I thought he meant the shell on it. My external USB HDD has the ground connection carried right through to the mains earth pin. I have continuity all the way from the metal drive case.
Inside every computer is a line filter to prevent the switching power supply signals from going back out your AC mains, called conducted EMI. Inside that filter is a cap between NEUTRAL, HOT, and chassis GND, called a Y-Cap. That y-cap effectively centertaps your AC mains, but usually the PC case is connected to earth ground, almost equal to NEUTRAL, so you never measure any voltage there. If the GND terminal on the outlet to the PC is floating, well you can get a pretty healthy zap. I can just start to feel 12Vac so this 60-70Vac hurts a LOT! The size of the y-cap is set to just about provide a maximum of 2mA.
Now such filtering on an isolated DC supply [if the whole thing is DC isolated from the PC chassis] can also cause the metal housing's voltage to meander around.
For what it's worth, 'hospital grade' leakage is less than 100uA and 'direct onnection to patient' hospital grade leakage is less than 10uA ...to simulate what that feels like the next time you're in a store with fluorescent lighting inside a metal trimmed display cabinet. Gently slide the back of your knuckles along the metal. You probably will feel the AC mains voltage. Now, *if* you touch an open wound to that metal! That's a big oweey, hurts like h---.
The only concern I would have about finding strange voltages where not expected is that that may be a precursor to a failure mode that would then supply BIG voltage, as in lethal voltage, if/when something else happens.
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