(1) Subsection (2) of this section applies:

(a) When it is deemed advisable to enlarge the boundaries of a district by the advisory committee for a district where special assessments have been or will be imposed; and

(b) If the conditions mentioned in section 39-1639 apply to such enlarged territory.

(2)(a) A petition for the enlargement of such district that is signed by persons that own not less than twenty-five percent of the territory proposed to be added to the district may be filed with the county clerk.

(b) If a petition is filed pursuant to subdivision (a) of this subsection, the board shall proceed as provided in sections 39-1640 to 39-1643, so far as applicable.