The board of trustees or the administrator shall not cause to be assessed for any of the improvements herein provided, property by law not assessable, or property not included within the district defined in the preliminary resolution, and shall not assess property not benefited; Provided, in cases when such exempt property has been specially benefited by the improvements, the owner of such property shall pay the district a sum equivalent to the amount the property has been specially benefited, which amount may be recovered by the district in an action against the property owner. If the parties do not agree as to the amount of the special benefits, the amount may be determined by the district court in an action brought by the district for such purpose. The board of trustees or the administrator may find that any part or all of such improvements made are of general benefit to the district except that the board or administrator shall levy special assessments on all lots, parcels, or pieces of real estate specially benefited to the extent of the special benefits to such property. The cost of such improvements shall be paid from the assessments levied against all the property in the district, in the manner provided by section 31-755, or may be paid from unappropriated money in its general fund. The cost of the improvements shall draw interest at the rate of six percent per annum from the date of acceptance thereof by the board or administrator until warrants are issued in payment of the contract price.