Court fines are normally considered a "priority debt," which means that they must be paid in full through any Chapter 11 repayment plan. You cannot discharge a priority debt without full payment.
Generally, court fines are not dischargeable in a bankruptcy case. Most individuals who owe court fines would not file a Chapter 11 case as the provisions of Chapter 11 are really most helpful for businesses that hope to reorganize and move forward as a going concern, large corporations (think United Airlines or Lehman Bros.), or people who do not qualify for the provisions of Chapter 7 or 11. Keep in mind that as an individual, you can set up a repayment plan for your court fines in a Chapter 13 case. I do not practice in Ohio, so you would be well advised to contact a knowledgeable and experienced bankruptcy attorney in Ohio. Although bankruptcy is a federal law, many of your rights and obligations are specific to your state and even to the specific area you live in, so it is very important that you contact an attorney in your area.