If such local improvement district is initiated by petition, such petition shall set forth the nature and territorial extent of the proposed improvement requested to be ordered and the fact that the signers thereof are the owners (according to the records of the county auditor) of at least fifty-one percent of the area of land within the limits of the local improvement district to be created. Upon the filing of such petition the board of park and recreation commissioners shall determine whether it is sufficient, and the board's determination thereof shall be conclusive upon all persons. No person shall withdraw his or her name from the petition after it has been filed with the board. If the board shall find the petition to be sufficient, it shall proceed to adopt a resolution declaring its intention to order the improvement petitioned for, setting forth the nature and territorial extent of said improvement, designating the number of the proposed local district and describing the boundaries thereof, stating the estimated cost and expense of the improvement and the proportionate amount thereof which will be borne by the property within the proposed local district, and fixing a date, time and place for a public hearing on the formation of the proposed local district.

The resolution of intention, whether adopted on the initiative of the board or pursuant to a petition of the property owners, shall be published in at least two consecutive issues of a newspaper of general circulation in the proposed local district, the date of the first publication to be at least fifteen days prior to the date fixed by such resolution for hearing before the board.