They want to see if the certificate is a forgery. If it is legitimate, there isn't really a reason why it wouldn't be in their system or records. If it is legitimate, and there is a valid reason why it wasn't put into the system, then you are still married, and you cannot ask them to not record it. But, if it's not legitimate, then you aren't legally married. Assuming you were married afer 1958, there is no common law marriage in Indiana. You need to discuss this with a local attorney to fully explore the other issues that may be raised if your marriage is not legal.
This answer is not to be considered a response to a specific legal issue in a specific jurisdiction - it is to be considered only a general response to a hypothetical scenario posed by the questioner. For specific legal advice, please consult with a licensed attorney in your jurisdiction.