There could be several reasons for which a copy of an official document may be requested. Broadly speaking, it could be needed for either personal or official purposes.
Personal: A person may have lost an important document, which has been allotted by some statutory authority or organisations viz. educational institutions, previous employers, government offices, etc.
Official: An officer of an organisation may request an officer of another organisation to provide a copy of the official document which was either corresponded earlier between them or which is an important piece of document needed by them for some official purposes.
The format of the letter would be almost the same in both cases. Important thing is to mention the required information about that document completely so that the person who is going to track it or provide a copy of it - should not face any trouble locating it because of any confusion.