This is powdery mildew, which is a regular occurance for some plants in our area. The disease load varies from year to year, but it generally starts to occur during warm days and cool, humid nights.
Here is a page about it: http://www.extension.umd.edu/hgic/powdery-mildew-annuals-bulbs-groundcover-perennials-and-vines

Part of disease management is trying to keep up good airflow, and reduce the amount of time that leaves stay wet.  
In this case, we really recommend either increasing sunlight to this area, or transplanting your crape myrtle to another part of your yard that has full sun.  Crape myrtles need full sun to do their best, and often do not produce blooms without it.

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