Welcome to ATP, giraffe71!!! Happy to have you here!
Yes, some Crape Myrtle trees' bark naturally peel or exfoliate.
Here is some information on the handsome Crape Myrtle:
http://www.clemson.edu/extensi...
I always admire the peeling bark. ;)
You can also read more here on our database and see photos from our members
The Crepe Myrtles Database
If you know the name of your variety, you can look it up on our ATP database.
Just click on the Plant Database tab at the top of the page and enter the name of the plant in the search box.
Hope this helps some!
Thanks for your question!