Carson City follows Nevada state licensing law, and the county or its cities issue the building permit for the job. Below: the state rule, the places inside the county, and live local coverage.
Nevada requires a contractor licence from the State Contractors Board, and overhead/garage doors have their own subclassification - C-3d Overhead Doors - with only a narrow under-$1,000 repair exemption that disappears the moment a building permit is required.