If an improvement has been or hereafter shall be established, constructed, or maintained pursuant to the provisions of this chapter, the board of flood irrigation, even after the benefits therefor have been assessed, shall have the power, either upon its own motion or upon the request of any interested property owner within said improvement district, and after said improvement has been established and constructed, to examine into and determine whether any property located within said improvement district has not been assessed for benefits. If such board shall find and determine that such property has not been assessed for benefits and in fact has benefited by the establishment, construction, and maintenance of such improvement, it shall proceed to assess such property for such benefits. After the improvement has been established and constructed, the board likewise, upon petition of an owner, may re-examine the benefits thereof. If it appears from such re-examination that more property of such owner has been assessed than actually has been benefited, the board may reassess such benefits so as to conform to the proven facts. All assessments made under this section otherwise shall be     made and reviewed in the manner provided in sections 61-12-22 through 61-12-24. If additional assessments are made pursuant to this section, the amount thereof shall be used, first to pay deficiencies in the cost of said project, if any, and the balance thereof, if any, shall be credited equitably and ratably upon the last payment of the assessments made upon the property originally assessed.