Thanks for writing. I'd guess the white spots you're seeing is a very common disease called powdery mildew. Unfortunately, it's very difficult to treat powdery mildew once it's attacked. You can try a fungicide --- this will help stop the disease from spreading any further.
Also: It's really helpful to prune your crape myrtle so air can flow freely through the branches -- this can also help deter the disease.
Other than that, there's not a lot you can do. If your crape myrtle is quite old, you may think about selecting a more mildew-resistant variety if you choose to replace the tree when it succumbs to old age.
---Justin, Senior Garden Editor, BHG.com