If it's not on a pedestal, it's bolted to the wall. The bolts are underneath and may be difficult to see, so don't hurt yourself contorting to see it. You may be able to find the cracks just by using your fingers to feel "lines" of water along the back of the bowls and near the faucet.
I don't really know how your management company works, but they almost certainly have to replace a cracked sink because it will eventually structurally fail and fall off the wall. Now, whether you want them to is another thing because management companies are notorious for blaming tenants for fixtures they didn't break.