You might buy an outlet tester and see if your hot/neutral are reversed or if ground isn't connected. If it all checks out you can use a multimeter* to check potential between neutral and ground. If your apartment is wired correctly there should be almost no voltage between the two.

At the breaker box the neutral and ground are supposed to be bonded together. That means only minor induced charges inside the building wiring would show up between the two. If there is any significant voltage then something is leaking on one of the lines or ground might not be bonded... it could even be floating if they didn't bother driving the grounding stake deep enough and the soil dried out a bit.

> At the breaker box the neutral and ground are supposed to be bonded together.

Note this advice is country-specific. In some countries, the bonding is done further away from the house.

In any case, you should never trust the neutral line to be an earth. If a fault occurs that disconnects the neutral line from the supply, your neutral line will have deadly voltage on it by virtue of being connected to live through your appliances. Moreover, depending on the multimeter you use, if you measure the voltage between neutral and earth, you could possibly trip the RCD in the distribution unit (if you have one).

The rules are simple in most countries - if it has any touchable metal parts, it must be earthed.