Declining an offer should be done in writing and as soon as you accept another position. This is an important step because you may need this contact later on, so never burn your bridges.
Sample Letter
50 Pine Tar Tree
Stowe, PA 19454
May 1, XXXX
Ms. Raquel Smith
Department of the Interior
Louisiana Street
Washington, DC 99887
Dear Ms. Smith,
Thank you for the offer that you extended for a position as a research assistant in the Department of Interior Extension Library. This offer was very attractive, and I had much to consider in reaching my decision.
You have an impressive organization and there are many aspects of the position that appeal to me. After much thought, however, I have decided to take a position in the Library of Congress. Their specialized resources and location in Washington, where my family resides, were the deciding factors in this difficult decision.
I appreciate your interest in me and wish to express again my gratitude for your courtesy and consideration.
Sincerely,
Joseph Brown