At or before the time of the passage of the ordinance directing that the improvement shall proceed, the Council shall determine whether the claims for damage so filed shall be judicially inquired into before commencing, or after the completion of, the proposed improvement.  If it decides that the damages shall be assessed before commencing the improvement, the Director of Law shall then make such application and such proceedings shall be had thereon as are provided by statute relating to the assessment of damages on such claims.  If the Council determines to assess the damages after the completion of the improvement for which a claim for damages has been filed, the Director of Law shall within ten (10) days after the completion of the improvement make written application and the same proceedings shall be had as hereinbefore provided.  No person who claims damages arising from any causes shall commence a suit therefor against the City until sixty (60) days after he shall have filed a claim for such damages with the Board of Revision.  This provision shall not apply to an application for an injunction, or other proceedings, to which it may be necessary to resort in case of urgent necessity.