When the state or any of its agencies is an applicant, petitioner or moving party commencing a matter in a Probate Court, or is otherwise liable for the fees or expenses under sections 45a-106a to 45a-112, inclusive, the court shall accept such matter without the filing fee accompanying the filing thereof, and shall bill the filing fee or other fee or expense to the appropriate agency for subsequent payment, which payment shall be due and payable upon receipt of such bill.