Question: If a Bard has concerns that a statue or corpse is actually a dormant construct or an undead, can they cast the Message cantrip, and target the statue/corpse to determine if either is indeed a creature?

The Spell Target is "one creature/level". The Saving Throw & Spell Resistance is "none" and "no".

Answer: 
The [*message*](https://www.d20pfsrd.com/magic/all-spells/m/message/) spell doesn't provide feedback
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A caster doesn't know automatically when he's cast a spell on an invalid target; instead, nothing happens and the spell just fails. (On [Spell Failure](https://www.d20pfsrd.com/Magic/#TOC-Spell-Failure) says, "If you ever try to cast a spell in conditions where the characteristics of the spell cannot be made to conform, the casting fails and the spell is wasted.") And that failure could've come about due to a variety of circumstances.

The only feedback a caster typically receives from *any* spell is the feedback from a spell that has both a *Target* entry and has a *Saving Throw* entry other than *none*. In that case, the caster learns *only* if the target succeeds on the saving throw against the spell. Other information must be gleaned from observation, special abilities, and as the result of the spell itself coming into effect. (See also Magic on [Saving Throws](https://www.d20pfsrd.com/Magic/#TOC-Saving-Throw).) (Note that the *message* spell has a *Saving Throw* entry of *none*; further, were the spell to have, for example, the entry *Saving Throw: Will negates*, an invalid target just wouldn't make the saving throw—therefore neither succeeding nor failing—, and the caster would still receive no feedback.)

This means that the simple act of casting the spell *message* on the typical wholly inanimate and totally-not-a-creature corpse or statue does not somehow provide feedback to the caster that reveals the spell failed—the caster lacks a heads-up display that flashes *Invalid Target*, for instance. However, because a typical wholly inanimate and totally-not-a-creature corpse or statue can't and won't be *replying* using the effect of the *message* spell, the caster may still surmise that target's nature.
Probably Not
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A reading of the entry for this spell does not specify that the caster knows if the message is failed to be received, however if the target talked back to you, using its option to do so, it would certainly give it away. The overview rules on magic do not specify that you have any knowledge of the spell failing that I could find (unless the creature passed a saving throw against a targeted spell, and message does not offer a saving throw), so I would say, in general: No, you couldn't use this to determine if a statue or corpse is a creature reliably.