Idaho Code § 33-304
In any joint district, the duties imposed upon, and the records required to be kept by, the county commissioners or any other county officer, in respect to school districts, including the assessment of taxable property and the levying of and collection of taxes, shall be performed or kept by the commissioners and other county officers in each county in which the district lies as though the portion of the district in each county were a separate district therein.
One (1) of the counties in which a joint district lies shall be the home county of the district.
When a joint district is created by the division of a county, or through the annexation of any territory by the state board of education, the board of trustees of such district shall designate its home county and give notice thereof to the state board of education and to the board of county commissioners in each county in which the district lies.
Idaho Code § 33-304