§1. Whenever the death of a spouse cannot be proven by an authentic ecclesiastical or civil document, the other spouse is not considered free from the bond of marriage until after the diocesan bishop has issued a declaration of presumed death.
§2. The diocesan bishop is able to issue the declaration mentioned in §1 only if, after having carried out appropriate investigations, he attains moral certitude of the death of the spouse from the depositions of witnesses, from rumor, or from evidence. The absence of a spouse alone, even for a long time, is not sufficient.
§3. The bishop is to consult the Apostolic See in uncertain and complicated cases.
Source: Code of Canon Law (Vatican.va)