To identify primary sources associated with your piece, start by looking at the composer's works list in Grove:
Grove Music Online - Look up your piece to find date composed, original key, original scoring, extant alternate versions,
catalog number, library holding manuscript, references. Also note the any complete editions or thematic catalogs available for the composer.
New Grove Dictionary - The same information is available in print in the Music Library.
Répertoire International de Sources Musicales - Catalog of 850,000 records, most of which are music manuscripts dating from before 1800. Search this in addition to Grove.
Primary sources material identified may include:
Complete and/or scholarly editions are filed under M3 in the Music Library. You can browse the shelves or the online catalog.
To see if the Music Library holds any manuscript facsimiles, search by composer name and manuscripts; if available you'll see the following subject heading for the composer, for example:
You can also browse all of U of M's Manuscript Facsimilies using this link:
University of Memphis does not hold a large collection of manuscripts and most libraries do not lend them. But you can search WorlCat to discover nearby collections that may hold desired manuscipt (or manuscript facsimiles) of the desired composition.
J.S.Bach - Autographs and Original Parts at Bach Digital
Beethoven Haus Bonn - Manuscripts, first editions, letters and pictures from the museum's and library's collections
Brahms - Autographs, early editions, letters, and images
Online Chopin Variorum Edition - Online scholarly edition that draws on various primary sources
Aaron Copland Collection - Copland's music, photos and letters
Mozart - The complete, scholarly edition with manuscript fragments and sketches and scholary notes
Ignaz Pleyel Early Editions - Over 200 early printed and manuscript scores
Arnold Schoenberg Center - Autograph manuscripts, musical sketches and drafts, and corrected early editions
Schubert - Musical manuscripts, letters, and other primary sources
Robert Schumann - Music manuscripts and letters between Robert and Clara Schumann at the University of Bonn
Early Music Online - 300 volumes of 16th-century music from the British Library were digitised from microfilm.
Europeana - Online portal to European libraries and archives, including all national libraries.
Harvard Library Online Resources for Music Scholars - Links to a variety of digitization projects.
The Juilliard Manuscript Collection - Collection of 140 priceless autograph manuscripts, sketches, engravers proofs and first editions
Digital Image Archive of Medieval Music - Comprehensive catalog (with limited images) of European medieval polyphonic music
Music Manuscripts Online (Morgan Library & Museum) - Includes good quality images of works by J. S. Bach, Beethoven, Brahms, Chopin, Debussy, Fauré, Haydn, Liszt, Mahler, Massenet, Mendelssohn, Mozart, Puccini, Schubert, Schumann and others.
The Munich Digitization Center - Includes manuscripts, fragments, and other musical primary sources from various German composers
University of Washington Digital Scores Collection - Manuscript musical scores dating from the 17th through 19th centuries.