This is a basic example of a letter of request. A letter of request is typically written when you want to ask for an interview or a raise. I can also be used if you need specific information or if you need a third party to write a letter on your behalf.
For this letter, if you are just asking for an interview, there is no need to include a resume. If requesting a raise, be straight and to the point and thank your employer for taking it under consideration. If you need information, let the reader know why you need the info and thank them for getting it for you.
If asking a third party to write the letter, remind them how you know one another and the specifics that you would like to have in your letter.