According to Lewis Hill in his book Secrets of Plant Propagation: Starting Your Own Flowers, Vegetables, Fruits, Berries, Shrubs, Trees, and Houseplants, crapemyrtles can be propagated by leaf cuttings under mist, seeds, and softwood cuttings.
Michael A. Dirr in Manual of Woody Landscape Plants: Their Identification, Ornamental Characteristics, Culture, Propagation, and Uses says seed germinate best if given a 30- to 45-day cold treatment, softwood cuttings taken in late May, June, or July, and semi-hardwood cuttings will root. Softwood cuttings taken in July-August given an IBA dip of 1000 ppm will root in 3 to 4 weeks.
Crapemyrtle is easily propagated from hardwood cuttings taken during the winter. Take cuttings from growth made the previous summer. Cut pencil-size stem into 6 to 8-inch segments. Avoid weak, twiggy cuttings. Cuttings can be placed in prepared outdoor rooting beds. If this procedure is followed, select a section that can be watered conveniently. Thoroughly pulverize the soil to a depth of 10 to 12 inches. Add 4 to 5 inches of organic matter to the surface and thoroughly mix into the soil. Peat moss, leaf mold, and pine bark are useful for this purpose. Place the cuttings approximately 6 inches apart. Insert one-half the length of the cutting into the soil. Mulch with 2 to 3 inches of pine straw, leaf mold, or pine bark to conserve moisture. Keep watered during dry periods in the spring and summer. Fertilize the young plants with a balanced fertilizer, such as an 8-8-8 analysis, beginning in May. Apply at monthly intervals until August at the rate of one-half teaspoon per plant. The young plants can be transplanted to their permanent location during the winter.

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