Since I don't feel like taking up space in the thread about falling damage, here's a new thread. Flesh to stone, as an example, says that it turns you into a mindless, inert statue, which does suggest that you become an object. The important part is whether you gain a hardness of 8 and reduce damage by half but lose the ability to make saving throws and Acrobatics checks like a normal stone object would.
As an example, let's say that someone is petrified, then somehow he triggers a trap that requires a Reflex saving throw to avoid some damage. You could argue that since sleeping characters and characters who unknowingly drink a harmful potion also get to make saves, a petrified character still can even though he is mindless, since being able to react doesn't seem to be required to make a save. On the other hand, he's an immobile statue now, so you could argue that he doesn't get to save, he just halves the damage and deducts his hardness.
*pokes* *pokes* Yup, he's a stiff, Jim. Bereft of life, he saves no more. This is an ex-creature!
The only difference I see between 'dead' and 'petrified' is that the 'resurrection' spell is easier to come by, and there can be some argument that the soul doesn't actually shuffle off the mortal coil, depending on methodology of the petrification. I have been known to rule in some systems that petrification is just as lethal as a knife to the jugular, and that reversing it just gives you a resurrectable corpse. Considering that statue to be an object is only reasonable.
Way, way back in this thread, I was trying to figure out the logistics of rescuing a bunch of petrified by a cockatrice creatures. Petrified creatures seem to be a weird hybrid of "not completely an object, but not a normal creature either".
You get to make reflex saves even if you're paralyzed. You are treated as having a dex of 0, so that will affect your save. Sometimes a reflex save is simply being lucky enough to be in exactly the right place at the right time.
However, I'm fairly certain that you can't make Acrobatics checks when paralyzed.
To me, the important part is whether being reduced to half hit points makes you acquire the "broken" condition, entailing the possibility that important bits of you fall off, thereby screwing up most magical attempts to restore the creature to living flesh. Ditto with the "destroyed" condition, which could mean that you are completely split asunder or shattered into pieces.
Silly me didn't look up the petrified condition:
A petrified character has been turned to stone and is considered unconscious. If a petrified character cracks or breaks, but the broken pieces are joined with the body as he returns to flesh, he is unharmed. If the character's petrified body is incomplete when it returns to flesh, the body is likewise incomplete and there is some amount of permanent hit point loss and/or debilitation.
So the amount of complication is specifically mentioned in the condition. It doesn't solve the problem of "is it an object", but it does handle the healing aspect.
I don't think there are actually any rules that cover this specific question, but I would treat a petrified creature as an attended object with hit points equal to the creature's, and the hardness of stone. Doing it this way does a few things: firstly, it acknowledges that it is still a creature, by allowing it saving throws (though pretty poor Reflex ones); it also simplifies bookkeeping by not forcing you to track separate hit points for the object; and it properly addresses how being made of stone affects resistance to damage.