Contiguous territories may be annexed to organized abatement districts upon petition of a majority of the legal voters in the territory seeking annexation and of the owners of more than half, by assessed value, of the taxable property in such territory, or by written request for annexation of a designated area, submitted to the trustees of the existing abatement district and signed by all members of the board of county commissioners in which county the territory seeking annexation is located. For annexations that will increase the size of an existing contiguous district, there shall be no size restriction on the property being annexed. Noncontiguous areas shall not be annexed unless the area meets the provisions of section 39-2801A, Idaho Code. Upon receiving this petition or written request, the trustees of the existing abatement district must submit the question of annexation to the legal voters of the district at an election held subject to the provisions of section 34-106, Idaho Code.