As Joe wrote, ask your building inspector. It's a simple phone call, nothing to be scared of. If your area is subject to code, then yes, it's likely that you need a minimum of 5/8ths-inch fireboard.
Some locales are more restrictive...one of the towns near me requires two half-inch layers, each taped and mudded.
Even if you have no restrictions, why not put in 5/8ths? It's only a few dollars more per sheet.
One last thing...if you don;t have fireboard in the garage, there is a possibility of having insurance problems down the road, either in getting coverage, getting a premium reduction, or getting a claim paid, etc.