The laws relating to the manner of service of the notices, the filing of claims for damages, and the effect of failure to file the claims, shall apply to the notice provided in section 4957.20 of the Revised Code and to all claims for damages by reason of the proposed improvement. After the expiration of the time for the filing of the claims, the legislative authority of the municipal corporation, when claims have been filed within the time limited, shall determine by ordinance or resolution whether the claims are to be judicially inquired into before commencing or after the completion of the proposed improvement. Thereupon, the mayor, or village solicitor, or city director of law of the municipal corporation shall make application for a jury in the manner provided by law to the court of common pleas or probate court of the county in which the municipal corporation, or the larger part of it, is situated, either before commencing or after the completion of the improvement, as the legislative authority determines. All proceedings upon the application shall be governed by the laws relating to the application provided for in other cases of city improvements.