I always thought 5/8 was code for a ceiling. I think I read that somewhere, or someone told me, I don't recall which. Is that wrong?
The IRC addresses ceiling thickness and states that 3/8 should not be used on ceilings which support insulation or where a water-based texture is used (1/2 and 5/8 is okay).
Where water-based texture is used, the sheet rock has to be run perpendicular to the joists; 1/2" can be no more than 16" OC, 5/8" no more than 24" OC.
However, you'd have to check in your municipality what codes, if any, apply.
Where I live there are no residential construction inspections unless it's required by your insurance. A friend and I built a 18x52 garage (long skinny lot) for some older friends of ours 2 summers ago and a $35 building permit was all we needed. No one, and I mean no one, from the city or county so much as stopped by to look at it. I thought they'd at least check the height or square footage, but nope.
An "inspector" from the owners' insurance company stopped right after we finished framing it but he was there for maybe 20 minutes. Walked around with a clipboard but that was it. No tape measure, no pictures, etc. Before he left he came up to us, asked if we were doing the roof (yes), and said he needed to make sure we use 7 nails per shingle. We said ok and he got in his car and took off. We live in thunderstorm and tornado alley, and I'm pretty sure roof claims are insurance companies' biggest headache around here.
From the time I've spent in California I'm pretty sure you have to get Vladimir Lenin himself to sign off if you want to change the color of your curtains, so you might want to check into it.