(a) Whenever any improvement shall be made upon any street occupied by the tracks of any railroad, the council is authorized and it shall be its duty to assess against such railroad situated within the improvement district its just proportion of the cost and expenses of making such improvement, which proportion shall be estimated on a basis of charging to said railroad not less than the cost and expenses of improving the space between the rails of said tracks, and for a distance of two (2) feet on each side of said rails. Said assessment shall be made on the rolls of said improvement district against the railway or railroad, the same as against other property, and said assessment shall be a lien upon said portion of said railroad from the time of the levy of the assessment by the council, and shall be collected in the same manner as other local improvement district assessments.
(b)  When any work or improvement herein authorized is done or made on only one (1) side of the center line of any street, assessments to cover the cost and expenses of such work or improvement may be levied on the lots and lands on that side only or on both sides, in amounts on each side as the council shall determine based on the benefits resulting to the property on each side.