An annulment simply recognizes that a valid marriage never existed, it does not dissolve a valid marriage. My assumption, based on your question, is that your marriage was one in which a Catholic married outside of the Church without a dispensation from canonical form. In the situation you describe, the decree of nullity (i.e. annulment) is done without the need for witnesses or testimony. You simply need to provide the evidence that a Catholic was married outside the Church without proper dispensation. The simplest way to do this is provide recently issued baptismal certificates of the Catholic party(s) and a copy of the marriage license. The diocese will then issue a decree of nullity on the grounds of lack of canonical form.
