An existing public hospital district upon resolution of its board of commissioners may be divided into two new public hospital districts, in the manner provided in RCW 70.44.350 through 70.44.380, subject to the approval of the plan therefor by the superior court in the county where such district is located and by a majority of the voters voting on the proposition for such approval at a special election to be held in each of the proposed new districts. The board of commissioners of an existing district shall by resolution or resolutions find that such division is in the public interest; adopt and approve a plan of division; authorize the filing of a petition in the superior court in the county in which the district is located to obtain court approval of the plan of division; request the calling of a special election to be held, following such court approval, for the purpose of submitting to the voters in each of the proposed new districts the proposition of whether the plan of division should be approved and carried out; and direct all officers and employees of the existing district to take whatever actions are reasonable and necessary in order to carry out the division, subject to the approval of the plan therefor by the court and the voters.