I live in an apt with no ground (built in the 40's).
10-06-10: Rotelmania
Multi story apt building? Good chance the electrical branch circuit wiring is installed in metallic conduit.
If you have a multi meter you can check it out.
*pull the receptacle outlet cover plate.
*Set the meter to AC volts.
*Insert one test probe in the screw hole that holds on the receptacle outlet cover plate. Or touch it to the one of the screws that holds the receptacle to the metal rough-in box.
*Insert the other test probe in the hot contact hole of the receptacle. Don't know which one is the hot one? Try both.
Meter should read 120Vac nominal....
If it does you have an equipment ground. How good of a ground? That depends on the integrity of all the fitting connections from the receptacle metal box all the way back to the electrical panel.
Hire an electrician he can test the ground conductivity by putting a temporary load across the hot conductor and the metal receptacle box. He will then check for voltage drop across the temporary load.
Have a new grounding type receptacle ready for the electrician to install if the equipment ground checks out ok.....
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