Be sure to take a look at information on herbicide injury and the diagnosis of same. Many links and photos, such as:
I am not sure there is a good chemical test to determine if it was herbicide injury--if there is, and the herbicide has not been metabolized and broken down--I suspect any test would be very expensive.
And the most important disease on smoke tree:
Verticillium wilt. Symptoms are fairly close. See also notes about how it is intolerant of poor drainage and high temperature of the roots. And dangers of mulch piled around the trunk.