Experts and BHG readers answer.
Thanks for writing. Because many varieties of crape myrtle can suffer from powdery mildew so badly, I'd prune the plant to keep it relatively thinned so there's good air flow. The best time to prune is in early spring, just before or as the tree begins to leaf out.
Unless you have poor soil, fertilization probably isn't necessary. If you do have poor soil a general-purpose fertilizer in spring can help the tree. Or, have your soil tested; a good soil test will tell you all about your soil so you don't have to buy fertilizers that apply nutrients your plants aready have enough of.
---Justin, Senior Garden Editor, BHG.com