California Code, Government Code - GOV § 65901

(a) The board of zoning adjustment or zoning administrator shall hear and decide applications for conditional uses or other permits when the zoning ordinance provides therefor and establishes criteria for determining those matters, and applications for variances from the terms of the zoning ordinance. The board of zoning adjustment or the zoning administrator may also exercise any other powers granted by local ordinance, and may adopt all rules and procedures necessary or convenient for the conduct of the board's or administrator's business.

(b) In accordance with the requirements for variances specified in Section 65906, the legislative body of the city or county may, by ordinance, authorize the board of zoning adjustment or zoning administrator to decide applications for variance from the terms of the zoning ordinance without a public hearing on the application. That ordinance shall specify the kinds of variances which may be granted by the board of zoning adjustment or zoning administrator, and the extent of variation which the board of zoning adjustment or zoning administrator may allow.