Do I need a permit for patio cover or carport in Green Bay?

Most likely yes. Patio cover or carport usually requires a permit in Wisconsin. Confirm the specifics with Green Bay.

Carports, porches and similar structures attached to a home built on or after June 1, 1980 are within the UDC under SPS 320.02(1)(g). Detached garages and other detached accessory buildings are outside the UDC except for the fire separation rules in SPS 321.08(1) (SPS 320.05(4)), so a freestanding patio cover or carport is regulated by local zoning and building ordinances. Wisconsin sets no statewide permit requirement for additions or alterations to existing homes; under SPS 320.09(2)(b) those permits are required where the local ordinance requires them, and in a municipality where DSPS has UDC jurisdiction building permits for additions and alterations are not required, though zoning and electrical permits may still apply. This patio cover attaches to the house or will have solid walls or windows. Attaching a roof ties into the home's walls or roof framing, and enclosing it with solid walls can turn it into a room addition. Both normally need a building permit with a framing plan, and an enclosed room may also have to meet energy, electrical and egress rules for living space.