You’re not dead when you’re petrified, either, which can lead to some pretty interesting exploits, rules-as-written.
Petrified creatures count as creatures, not objects, so rules-as-written you can determine if a statue is a petrified creature by trying to target it with a spell that requires a creature for a target.
With the cantrip Poison Spray, you can check for petrified creatures without using spell slots or risking damaging the creature, since it would be immune to poison while petrified.
You can also safely check with Vicious mockery. The spell can target any creature, but only damages the target if it can hear, which “inanimate” things cannot.
On the other hand, Dissonant Whispers causes the target to hear (rather than hearing being a precondition as it is with Vicious Mockery) and with this you can kill petrified creatures, thus ensuring no spell casters return them to flesh-and-blood, without damaging the statue.