A fungus or some types of mold, such as black spot will be on the leaves. Often crepe myrtles will have lichens growing on the bark. If it is lichen, it will not harm the tree. Some people, myself included, don't like the appearance of the lichen-covered trunks. While wearing garden gloves, I slide my hands up and down to remove the lichens. On the other hand, if what you have is a fungus, you spray with a fungicide. Also, be sure to remove any dropped leaves that have the spots from the ground below. If they are not removed, rain or irrigation will splash the mold spores back up onto the tree and any surrounding plants.