The best time to prune a crape myrtle is in late winter (February), prior to the start of new growth. Crape myrtles need very little pruning, and most pruning is only done for the sake of the owner’s aesthetic preferences. It is better to maintain a natural form by thinning out crowded growth. Thin growth by removing a few selected branches where they join another branch.
You can fertilize in the spring, after new growth has begun. Use a balanced plant food (5-10-10 or 8-8-8), broadcast over the root area under the canopy of the tree.