This sounds like the beginning of a joke, but the truth was that the statue was rather shy. It was a copper-burnished statue of Napoleon on a rearing stallion, with his finger pointed in the air triumphantly. Napoleon's finger, not the horse's. The grammatical phrasing of that earlier sentence makes it seems as if the pointing finger belonged to the horse, but we know that's ridiculous; the horse had hooves.
Unfortunately, the sculptor had been rather careless in his measurements and had made the horse's front right leg shorter in length than its left. You couldn't notice it when the horse was rearing, as its limbs were in a frozen flail. But when he was walking around, the negligence caused the statue to hobble around in an unsightly manner, which made him quite self-conscious. He was understandably more comfortable staggering around only around staggering drunks.
Of course, the fact that he didn't move in your presence unless you were past the point of buzzed really begged the question: if a tree falls in the woods and there's no one sober around to hear it, does it make a sound at all? And even if it does, will anyone believe you when you tell them so?
Another reason why the statue only moved in the presence of drunkards was because he rather enjoyed alarming them. Mainly he wanted to see them act just like the people do on sitcoms, when a hobo that's slumped on the street corner can't believe his eyes, rubs them roughly, and looks askance at the bottle in his hand. The statue rather liked formulating this suspicion between a drunk man and his moonshine wherein only a sort of fuzzy warmth and sweet comfort had existed formerly. All good relationships, after all, require a little bit of doubt.
He didn't want to alarm them to the point of making them give up alcohol completely. If his actions turned out to be more effective than Prohibition, then no one would get drunk. And then no one would see him move. And despite it all, he wanted to be seen.
There's something to be said about being regarded in amazement. Not just to be glanced at, but to be marveled at or to have your presence make a palpable impact on another soul. Very few people have ever felt truly looked at, and it usually takes a singularly special individual in your life to make you feel genuinely seen.
So when a drunkard was trailing home in the wee hours of the morning/night past the town square, the statue would scrabble like a crab down from its perch and scuttle unevenly across the cobblestones, much to the alarm of many a man or woman there to witness it in action.
Despite all its fun however, the statue did find its imposing existence rather lonely at times. As much as he was seen or marveled at, his existence was never taken very seriously and his sentience was more often than not doubted, which is a very difficult way to live.
But what was a poor, painfully shy statue to do?