It depends on your situation. If you are a non-Catholic who does not intend to become Catholic and are not contemplating marrying someone who is Catholic, you are not bound by Catholic marital law. If you are a Catholic or intend to become a Catholic or are contemplating marrying someone who is Catholic, you might need a Church annulment.
For those who are bound by Catholic marital law or for those in preparation to marry someone bound by Catholic marital law, the general rule of thumb is that the Church wants to look at any prior marriage that looks like it could have been a valid and/or a sacramental marriage. Consult with your local Catholic parish priest or a parish staff member he designates to help you determine if you need an annulment.
Because there is usually a lot of administrative work involved in the process and therefore a lot of expenses that are generated, applicants are expected to pay for such expenses. This is analogous to the court and legal expenses involved in obtaining a civil divorce. If you are unable to afford a fee, however, let the marriage tribunal know so that it can arrange with you a reduced or waived fee, depending on your particular circumstances.
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