Without prejudice (standard legal term, at least in the UK, meaning that the payment of compensation will not necessarily be affected) to payment of compensation in due time because of the damage/loss incurred, the Insurer may require attestations, or testimonial/statements from the competent authorities, as well as the results of inquiries, or even a copy of the testimonial/statement perhaps establishing the opening of the investigation.
Seth, my attempt, of course without seeing the whole context it is difficult, but I hope this helps. I think it may refer to an initial statement/report (given to police) reporting loss/damage/theft etc.. most insurers will not consider claims unless they have been reported to the police (whereupon the victim will receive a crime number).

Portuguese term (edited): copia da certidão de abertura de inquérito porventura instaurado

copia da certidão de abertura de inquérito porventura instaurado." => copy of the certificate of an investigation which happened to be opened

The "certificate of investigation" implies the opening thereof. There is no need to translate the "abertura", since the certificate of investigation is obviously only issued when the investigation has begun.

sugestão