“Special district” means any agency of the state for the local performance of governmental or proprietary functions within limited boundaries. “Special district” includes a county service area, a maintenance district or area, an improvement district or improvement zone, or any other zone or area, formed for the purpose of designating an area within which a property tax rate will be levied to pay for a service or improvement benefiting that area. “Special district” does not include a city, a county, a school district or a community college district. “Special district” does not include any agency which is not authorized by statute to levy a property tax rate or receive an allocation of property tax revenues. However, for the purpose of the allocation of property taxes pursuant to Chapter 6 (commencing with Section 95) of Part 0.5, and notwithstanding Section 2237, any special district authorized to levy a property tax or receive an allocation of property tax by the statute under which the district was formed shall be considered a special district.