How to root a crepe myrtle
How to prune and root for another crepe myrtle?
These articles should help: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/how-to-propagate-crepe-myrtle-trees.htm
What I have done is take clipping of new growth about 6-8 inches long and cut an angle from parent plant. Clip off lower leaves making sure to leave a few at the top of cutting. Where I cut the end I scrap along the sides and pierce through once with sharp knife and roll in honey as a rooting hormone (honey has done amazing for me!). I then plant the cutting in premoistened seed starter soil and cover with plastic making sure not to touch the leaves with it for it will make them rot OR I cut a liter bottle in half and put holes in bottom fill with soil and replace the top with out the cap and place it out of direct sunlight aka a shaded area preferably on the north or south area of home. Then once a day I use a spray bottle to mist the clipping to keep it moist. Wait about a month or longer and gently give the leaf a tug and if you feel resistance than you have roots growing.