In Ohio, you can't get information of that sort from a defendant using the court process before a judgment is entered. However, as one previous answer suggested, sometimes answers to discovery about the circumstances of the lawsuit will reveal leads to assets.
Once a judgment is entered, as another commenter noted, you will have some court-provided processes for discovering the debtor's assets, such as a "debtor's exam," where the debtor is forced, under oath to answer questions about their assets.
Using tools other than the court process typically provides an incomplete picture of assets. Generally speaking, it is much more difficult to find out information about assets held in banks in 2012 than it was a few years ago, due to the passage of the Gramm-Leach-Bliley Act, which placed some limitations on the ability of private investigators to access bank information. Be skeptical of services that can promise you bank balances.
Aside from hiring a PI, the easiest asset search that you can do on your own is to search the land records for Cuyahoga and surrounding counties for real estate owned by the potential defendant. Check the websites for the County Auditor or Fiscal Officer, and look for a real estate search.
There are many companies/organizations who perform asset searches for a fee. Many private investigators also perform these types of searches.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
In addition to private firms that will do asset searches for a fee, once a party is involved in litigation, it is subject to discovery which may reveal such information. Additionally, at the conclusion of the litigation, if a money judgment is issued, the prevailing party may ask for a debtor's exam or other court ordered discovery that it geared to locating assets. If you have a lawyer, the lawyer should be aware of these options.
I have been licensed to practice in the State of Oregon since 1990. I am not offering legal advice regarding your question, only general information regarding the law. You are not my client nor am I your attorney unless we sign a retainer agreement.
Hire a good private investigator. But be prepared to spend at least $1000 - $2000 for a good asset search.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.