Q.branches falling off crepe mytrle tree
Early spring branches falling off crepe myrtle trees.

Improper pruning can leave the Crepe Myrtle with weak branches and that could fall off.
Does the tree have knots on the branches? This cold be Crepe Myrtle Knot.
Here are some links with more information.
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-care.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-tree-problems.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/fix-crepe-myrtle-knots.htm