It is the killing curse, it is meant to end life. What happens when it hits something that was never living? The dubious Harry Potter wiki seems to imply that objects might explode or otherwise be destroyed. Why would that be?
We see several cases of AK hitting inanimate objects in Order of Phoenix, with varying effects, during battle in the Ministry:
But the headless golden statue of the wizard in the fountain had sprung alive, leaping from its plinth to land with a crash on the floor between Harry and Voldemort. The spell merely glanced off its chest as the statue flung out its arms to protect Harry
... spat Voldemort. He sent another killing curse at Dumbledore but missed, instead hitting the security guard’s desk, which burst into flame.
Another jet of green light flew from behind the silver shield. This time it was the one-armed centaur, galloping in front of Dumbledore, that took the blast and shattered into a hundred pieces,...
From this we can infer that SOME objects will be critically damaged (from set on fire to exploded in pieces), but NOT always.
However, we see OTHER things explode from spells that aren't (necessarily or at all) AK:
He skidded around another corner and a curse flew past him; he dived behind a suit of armor that exploded. (HBP, Chapter 28: Flight of the Prince)
Since JKR usually very explicitly shows Avada Kedavras (by name or green color), this was most likely NOT AK.
"You won't say no? Harry, obedience is a virtue I need to teach you before you die. . . . Perhaps another little dose of pain?" Voldemort raised his wand, but this time Harry was ready; with the reflexes born of his Quidditch training, he flung himself sideways onto the ground; he rolled behind the marble headstone of Voldemort s father, and he heard it crack as the curse missed him. (GoF, Ch 34)
This was definitely not AK, but it cracked a slab of marble.
"Well, the big Death Eater had just fired off a hex that caused half the ceiling to fall in, and also broke the curse blocking the stairs," said Lupin (HBP).
This was referred to as a hex, so not AK which is a curse (and Lupin knows the difference)
From this, we can't get an unequivocal answer, but it seems that
1) AK doesn't necessarily destroy ALL inanimate objects it hits. But it's quite prone to doing damage.
2) Whatever it does destroy, MIGHT be due to the general power of the spell as opposed to the spell being AK specifically, as other powerful spells have similar effects.