Upon receipt of an owner's petition meeting the conditions established in § 37.01(B), the Council shall hear such petition and the arguments for and against the same and grant or refuse such petition as it may see fit. Such hearing must be had not less than 5 and not more than 30 days after the filing of such petition. If the Council decides to grant such petition, the property must be annexed by ordinance. The Municipal Secretary shall file a certified copy of the ordinance annexing the property together with a duplicate copy of the petition in the office of the County Clerk.