A municipality may construct street or road improvements outside its jurisdiction with the consent of the affected township, or if the property is located in unorganized territory, the county. When property is brought within the corporate limits of the municipality, the municipality may subsequently reimburse itself for all or any portion of the cost of the improvement for which municipal funds have been expended, by levying an assessment upon any property abutting on, but not previously assessed for, the improvement. No assessment may be so levied unless the property to be assessed was given notice and hearing of the improvements under section 429.031 at the time the improvement was ordered, and subsequently in accordance with the notice, hearing, and appeal rights, provided for under sections 429.061 and 429.081.