Those are tiny drip of honeydew excreted by crape myrtle aphids (see next question). Why are my crape myrtles leaves so shiny and sticky?
That is honeydew being secreted by crape myrtle aphids. Look closely at the newest leaves and you will see the small, pear-shaped pests congregating. Use a general-purpose insecticide to stop them at first evidence of their arrival, generally in late July or August. Left unchecked, they will secrete enough honeydew to coat the leaves completely. Black sooty mold will grow in the sticky layer, disfiguring the leaves and even causing premature defoliation in late September or October. However, the plants will come back the following spring so that the cycle can begin all over again. How do I start new crape myrtle plants? Can I grow them from the seeds? Answer: Since crape myrtles are hybrid plants, they will not “come true” from seeds. Probably one plant in several thousand would be of quality enough to keep. Nurseryman start new crape myrtles by taking cuttings either in late winter (hardwood cuttings) or in May (softwood cuttings). See the discussion on crape myrtle propagation.