American dogwood is susceptible to a fungal disease called anthracnose that is a leaf spot disease. It's hard to tell without pictures.
In order to get a good diagnosis quickly, I recommend you take samples to your local Penn State Extension where they will send it to the Penn State Plant Clinic for diagnosis

Eileen,

Thanks for your response.  I have attached pictures of the white mold on some branches and the green moss on others.  I'd appreciate any advice you have on how to keep this dogwood tree healthy.  The tree is about 45 years old.

Thanks!

The blue green growth is lichen and is natural in the forest. It has no roots and does no harm. The middle picture is a green moss or mold. If you scrape some off you will see that it isn't rooted in the bark. These organisms appear on bark when the weather is damp but they don't penetrate the tree. The white growth is also some kind of slime mold called the blob. As long as the bark isn't penetrated, the organism isn't harming the tree. Here is a link to an article about slime molds.