(b) Within ten days after the local law becomes effective, the municipal clerk shall, in addition to any other filing required by law, cause a certified copy thereof to be filed in the office of the state comptroller at Albany, New York, and within two weeks thereafter shall cause a copy of the local law or a summary thereof to be published at least once in the official paper or newspaper of general circulation in the municipality.

(c) This local law shall be final and conclusive unless a proceeding to review is commenced in accordance with this subdivision. Any person aggrieved by any local law adopted pursuant to this article may seek judicial review of the local law in the manner provided by article seventy-eight of the civil practice law and rules, provided the proceeding is commenced within thirty days from the date of the publication of the copy or summary of the local law pursuant to subdivision (b) of this section. No review shall be had unless the petitioner shall give an undertaking approved by the supreme court, or a justice thereof, as to form, amount and sufficiency of sureties, that, in the event of failure to modify the local law he will pay to the municipality, all costs and expenses as are incurred by it on account of the proceedings, as shall be determined by the court. In the event that upon this review there shall be any modification by the court of the local law, the court shall direct the modification by judgment which shall be final and conclusive, and the municipal clerk shall cause the judgment to be recorded and filed in the same places and manner as was the local law which was modified.