You did not mention the type of dogwood. It is normal for the bark on Kousa, Chinese dogwood to exfoliate. Other reasons for bark peeling include drought, poor drainage, excessive mulch, wildlife damage, etc. See our publication on these types of problems http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG86%20Common%20Abio...
Dogwoods in general are subject to a lot of stresses and can be susceptible to insects (borers) and disease issues. See our dogwood publication http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG12_IPM_Series_Dogw... You can send us digital photos of the whole tree, around the base of the tree, and affected trunk area so we can see what you may be dealing with. mh