Over the course of his long career, Elliott Carter produced an enormous documentary legacy including sketches, scores, recordings, letters, photographs, concert programs, newspaper and journal articles, interviews, films, memorabilia, and so forth.
Before 1988 much of this material was housed at the Music Division of the New York Public Library and at the Library of Congress in Washington, D.C. A substantial number of items were given to these libraries as gifts and remain there today. Other materials (including almost all materials at the New York Public Library) were left on deposit until 1988, at which time Carter sold them to the Paul Sacher Foundation in Basel, Switzerland. The foundation now owns the majority of the Carter materials pertaining to Carter’s career from 1988 until his death in 2012, as well as many earlier materials, all of which must be consulted on the foundation premises. The foundation makes available a limited number of research grants to scholars who wish to travel to Basel to study their collections. More information is available at the Paul Sacher Foundation website.
Carter donated the majority of his papers from 1932 to 1971 to the Library of Congress in Washington, D.C. According to the library’s resource description, the collection
…begins with 200 pages of counterpoint exercises from the early 1930s when Carter was studying with Nadia Boulanger in Paris and ends with the holograph score and 2,400 pages of sketches for his String Quartet no.3 (1971) which earned Carter his second Pulitzer Prize. Also included are holograph scores and voluminous sketches for: Canonic Suite; Piano Sonata (200 pages of sketches); Minotaur Suite; Emblems; Woodwind Quintet; Cello Sonata (400 pages of sketches); Eight Etudes and a Fantasy; String Quartet no.1 (550 pages of sketches); Six Pieces for  Kettledrums; Sonata for Flute, Oboe, Cello and Harpsichord; Variations for Orchestra (1,500 pages of sketches); Double Concerto for piano, harpsichord and two chamber orchestras (4,000 pages of sketches); Piano Concerto (7,500 pages of sketches); and other works…. 1,735 leaves of sketches for the Concerto for Orchestra dating from this period are not included in this collection but are available on microfilm in the Performing Arts Reading Room.
Most of the Elliott Carter Collection at The Library of Congress has been digitized and is available free of charge online. The collection contains sketches and other autograph materials for a number of compositions, including Symphony No. 1, Emblems, Woodwind Quintet, Eight Etudes and a Fantasy, Sonata for Violoncello and Piano, String Quartet No. 1, Sonata for Flute, Oboe, Cello and Harpsichord, Double Concerto, Piano Concerto, and String Quartet No. 3, and may be found at the Library of Congress’s website in the Music Division’s Elliott Carter Collection.
The New York Public Library has a collection of clippings and programs, correspondence, photographs, an interview transcript, and Carter’s 1994 Grammy nomination medal. See Elliott Carter papers 1945-1995.