Powdery mildew is one of the most common problems of crape myrtle. Preventitive measures for your tree is giving it full sun - 6 hours minimum a day and good aeration around the plant. Primarily this disease happens during spring (disease development favored by succulent new growth during warm days, cool nights with extended period of dry weather). May also occur throughout the growing season. The spores and mycelia of powdery mildew are sensitive to extremes of heat and sunlight. Counter-intuitively, rain does not increase the likelihood of powdery mildew, as the spores do not thrive in water.

There ae cultivars of Lagerstroemia that have a resistance to powdery mildew. Many have Native American nation names, such as “Catawba” (purple flowers, 15 by 15 feet), “Cheyenne” (red flowers, 10 by 10 feet) or “Natchez” (white flowers, 20 by 20 feet).

Treatment:

Less toxic fungicides are available including horticultural oils, neem oil, jojoba oil, sulfur, potassium bicarbonate and biological fungicides. Except for the oils, these materials are primarily preventive. Preventive treatments are applied to susceptible plants before any sign of the disease.

More here: http://www.clemson.edu/extension/hgic/pests/plant_pests/flowers/hgic2049.html

Hope this helps.