There are several pest that actually will attack a Crape Myrtle that is stressed. If you have ever walked under a Crape Myrtle and be dripped on. It is not the tree, it is aphids or another insects secretions you are feeling. Generally, a healthy and non-stressed plant will not have these issues. Attached is a PDF file that will give you some answers to what is attacking your tree. 

Insect Pests of Crape Myrtles and Suggestions for Their Control