Either party can start the process. Both are given an opportunity to participate. The process will go on even if one refuses to participate. A person does not request an Annulment actually. They request the Tribunal to investigate the validity of the Marriage and issue their findings.
Only one party need desire the annulment. In fact, the other party may be quite uncooperative, but that does not impede the process. When I filed for an annulment, my Protestant ex-husband was quite unhappy about the fact. He was given an opportunity to provide his side of the story. I do not know whether he did so or not. But my previous marriage was declared null.
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