Out of context, you can't tell the difference.
The spell ends after 1 minute. RAW, there is no "lingering aura" to detect. In many cases, finding a perfectly realistic statue should prompt adventurers to ask questions: Why is this in the middle of an underground forest / cavern?
RAF, I don't think there is anything wrong with the DM's decision that the party can recognize that there is something magical about the statue, but I recently went on an adventure where statues of political dissidents were scattered throughout a city under martial law. The horror of the party's dawn when they realized that they were actually all people over the course of several sessions was worth it without knowing it initially.
In the situation you describe, the "perfectly realistic" can be used to help the party. If you can uncover mistakes in workmanship, differences in material (maybe the official statues are inlaid with metals or just carved from onyx), or have to solve some other logical puzzle, you can make the guessing game a memorable part. rescue rather than frustrating spell wastage.