In general, you do not need a permit to replace drywall in Texas. However, there may be some specific circumstances where a permit is required. For example, if you are making structural changes to the wall or if the work is part of a larger remodeling project that requires a permit, you may need to obtain a permit. It is always a good idea to check with your local building department to determine whether a permit is required for your specific situation. They can provide you with information on any applicable codes or regulations that must be followed and help you understand the permitting process.