If it came with Vista then you most likely have the 32 bit version. You could upgrade to a 64 bit version if you want, since the Core 2 Duo is a 64 bit processor.
Not trying to jack the thread or anything, but just wondering...
If you've already purchased a 32-bit version do they offer an upgrade to 64-bit for half-price or anything...or at least a discounted price? I'm assuming not, but just wondering.