The cost of such improvement, when the same shall have been ascertained, shall be assessed or apportioned by the Town Council, or by some committee thereof, or by any officer or board authorized by resolution of the Town Council to make such assessment or apportionment, between the Town and the abutting property owners when less than the whole is assessed, provided that, except when it is otherwise agreed between the Town and the landowner, that portion assessed against the abutting property owner or owners shall not exceed one-half of the total cost.

Notwithstanding any other provision of this Chapter, any portion of the cost of such improvements not funded by such special assessment may be paid from federal or state funds received by the Town for such purpose.