They can certainly bring the claim. Whether or not it stands is a different story. Consult a local attorney to review your documents and advise you.
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Just because you lost, doesnt mean it was malicious prosecution. Speak to your atty about the Mal pros rules in Ohio.
Call a lawyer in your area to review the case for you. There is not enough information in your post to give an answer and there are many factors that could influence the decision making process.
This response does not constitute legal advice and does not create an attorney-client relationship. Legal problems and solutions depend on their unique facts. Due to the complexity and ever-changing nature of the law and to the limitations of this forum, this information may not be complete or adequate for your specific situation. Laws and regulations often differ from one jurisdiction to another. Mark E. Barbour practices in the State of Ohio.