The flowers of dogwood trees (Cornus florida) are the small oblong forms in the center of the bloom, and they do have both male and female parts. Most of us think of the beautiful white 'petals' as part of the flower, but they are actually bracts, inside which the tiny flowers form.
There are several native tree species of dogwoods in the U.S., and most are under attack by a deadly disease, Distula destructiva, a form of Anthracnose. The Asian Kousa Dogwood(Cornus kousa), much more resistant to Distula, is now the dogwood of choice as a replacement for Cornus florida. Apparently it's wildlife value is comparable, but personally, I prefer the elegant form of our native species. Sometimes these diseases play themselves out, and I hope that is the case with Distula.