"Elaine, the black coating is sooty mold. It doesn't directly harm the plant -- rather, it is living on what's called honeydew, which is a sugary excretion of aphids that are feeding on your crape myrtle. It's what you thought was sap, which is an understandable mistake.
The key to getting rid of the problem, then, is to control the aphids. Find a reputable garden center in your area and tell them that you need to control crape myrtle aphids and they should be able to recommend a suitable control. The spray needs to be very thorough, covering all parts of the plant. A couple of sprays, a week or so apart should do the trick. "