A solid roof adds overhead shelter while retaining open sides, creating a different project from an uncovered deck or a basic slatted pergola. Adding a roof changes the loads carried by the structure. Posts, foundations, beams and the house connection need assessment before an existing deck is assumed suitable. The roof connection and water management also deserve their own design.
Think about daylight inside the house as well as shade outside. Roof shape, height and location can affect views from windows and the use of the deck below. Allow room for circulation, stairs and the furniture you expect to keep beneath the cover.
Greensboro includes new roofed areas in its residential site-plan requirements, including roofs over existing porches or patios. The actual authority and review steps depend on the address and proposed work. Bring these questions into the scope early. Describe the existing deck or proposed footprint, the height of the back door and the type of overhead shelter you want in your inquiry. Include any plans for screens, lighting or stairs so related work can be reviewed with the roof.