(1) An application for admission shall be made in writing by one of the following persons:

(a) If the person applying for admission has a court-appointed guardian, the application shall be made by the guardian; and

(b) If the person applying for admission does not have a court-appointed guardian and has not reached the age of majority, as established by section 43-2101, as such section may from time to time be amended, the application shall be made by both parents if they are living together or by the parent having custody of such person if both parents are not then living or are not then living together.

(2) The county court of the county of residence of any person with an intellectual disability or the county court of the county in which a state residential facility is located shall have authority to appoint a guardian for any person with an intellectual disability upon the petition of the husband, wife, parent, person standing in loco parentis to such person, a county attorney, or any authorized official of the department. If the guardianship proceedings are initiated by an official of the department, the costs thereof may be taxed to and paid by the department if the person with an intellectual disability is without means to pay the costs. The department shall pay such costs upon presentation of a proper claim by the judge of the county court in which the proceedings were initiated. The costs of such proceedings shall include court costs, attorneys’ fees, sheriffs’ fees, psychiatric fees, and other necessary expenses of the guardianship.