I am Japanese, don’t belong to any religion, didn’t convert to Judaism and had married a Jewish man. In order to get a divorce, I am required to submit a document to the law court that argues/proves that I am "chasrat dat". I am not 100% certain what is being asked of me. Could you please explain to me what or how I am supposed to argue/prove regarding my religious status? Thank you for your help.

I believe it would be sufficient to obtain a formal legal document from your embassy that attests to the fact that you are not Jewish and don't belong to any religion.