(a) In all cases where any municipal corporation shall be liable for the payment of damages to the owner or occupant of any lots or grounds, by reason of the grading of any streets or alleys, or public grounds, or part thereof, the damages shall be ascertained and assessed by three (3) disinterested reputable freeholders of the city who shall be appointed as follows:

(1) One (1) by the city or town council;

(2) One (1) by the owner of the property injured; and

(3) The persons thus appointed shall choose the third person.

(b) The assessors thus appointed, before entering on their duties, shall take an oath or affirmation, before some officer authorized to administer oaths, that they will well and truly, to the best of their knowledge and ability, appraise the damages which the claimant may or shall have suffered by reason of the grading, and for which the city is liable. This oath shall be filed in the office of the city clerk, and the assessors shall, within thirty (30) days after their appointment, make the assessment, and file it in the city clerk's office, where it shall be subject to the inspection of all claimants for damages. The damages assessed by them shall be by them paid out of the city treasury or tendered to the party in whose favor the damages were assessed.

(c) If the claimant refuses to appoint, the council shall appoint all three (3) of the assessors.

(d) If any person shall neglect or refuse to accept the amount so assessed, as provided in this section, and shall prosecute the city, and if by suit for damages he shall not recover more than the amount allowed by the assessors, the party so prosecuting shall pay all costs of suit.

(e) No claimant for damages shall commence any suit for damages on account of the grading or improvement until he shall have filed a claim for greater damages with the city clerk at least thirty (30) days before the commencement of the suit.

(f) No suit shall be commenced until after the assessors shall have been appointed and made return of their assessment as herein provided, nor for thirty (30) days thereafter.

(g) The city or town council, within three (3) days after the claimant shall have notified them in writing that he has appointed his assessors, shall appoint one (1) assessor on the part of the city. They shall, within five (5) days thereafter, select the third assessor and qualify him as provided in this section.