Check with your local building or permitting department. Often, they make exceptions for very small projects.
Keep in mind that even if you do not need a building permit for your small renovation project, you may still need an electrical, plumbing, or other permit. There are usually exceptions and subtleties to the rules, so it's always a good idea to give your local building department a call to make sure you're correct in your understanding that you don't need a permit.