Ky. Rev. Stat. § 104.510
At the time of filing the petition, or at any time subsequent thereto and prior to the time of the giving of notice by the secretary, as provided in KRS 104.530, the petitioners shall either file bond with the secretary with security approved by him, or deposit cash or securities with him in an amount sufficient to pay the costs in the proceedings thereafter involved. If the secretary at any time during the proceedings is not satisfied that the bond or deposit is sufficient or that the surety on the bond is safe, he may require the execution of an additional bond or the giving of additional surety or an additional deposit within a time to be fixed not less than ten (10) days thereafter, and upon the failure of the petitioners to comply, the secretary may refuse to proceed further and may refuse to organize the district.
KRS 104.510