"Pruning - Dogwoods seldom need pruning except to remove dead, injured, diseased, or insect-infested branches. If shoots should grow below the graft they should be pruned off. Lower branches may need to be removed to allow for gardening activities or to improve air circulation. Prune in the dormant season --- pruning in late spring could create an entry point for dogwood borers. Make pruning cuts back to the branch collar."

Here is a link that might be useful: NCSU

I would think IF the branch is dead you could take it out anytime of the year.

That is correct....deadwood pruning should be done whenever you notice it.