The page on Detect Magic states
Outsiders and elementals are not magical in themselves, but if they are summoned, the conjuration spell registers.
while the page on Golems states
Golems are magically created automatons of great power. They stand apart from other constructs in the nature of their animating force—golems are granted their magical life via an elemental spirit, typically that of an earth elemental.
So, with this information in mind, when one of my players targets a suspicious statue with Detect Magic to determine if it is a golem in disguise and it is in fact a Golem in disguise, what information does Detect Magic reveal?
In case it is relevant, the statue is not recently created. It has been in place for a few centuries.
Best Answer
No, they do not
Golems are created using very similar methods of creating magic items, but are not magic items themselves once created. They are creatures, instead, of type construct.
There is absolutely no reference in the rules stating that constructs, or golems more specifically, have a magic aura that could be detected. They are magical creatures, just like familiars and other magical beasts, but that doesn't mean they emanate a magical aura, which is what Detect Magic actually cares about. Not even the higher level version of the spell, Arcane Sight, will actually detect creatures as magical, but the magical auras affecting them and magical items they are carrying.
We also have clear exceptions to this, as Animated Objects if created using temporary magical effects (Animate Objects or Permanency) are stated to be susceptible to dispelling and anti-magic, while permanent constructs are not:
However, this doesn't mean that a specific golem cannot be detected if they have a supernatural ability like an aura (like a Cryptguard), or a constant magic effect (like the Graven Guardians). They are also identifiable by Knowledge (Arcana), and there are specific constructs that are made for the purpose of looking like a statue, like the Caryatid Column, Guardian Gargoyles and Cephalophore.
This has been confirmed by James Jacobs (Creative Director) on his Ask me anything thread: