"mortuary," 1821, from French Morgue, originally a specific building in Paris where bodies were exposed for identification:
Before that it was the place where new prisoners were displayed to keepers to establish their identification. Thus the name is believed to be probably from French morgue "haughtiness," originally "a sad expression, solemn look," from Old French morguer "look solemnly," from Vulgar Latin *murricare "to make a face, pout," from *murrum "muzzle, snout." The 1768 Dictionnaire Royal François-Anglois Et Anglois-François defines French morgue both as "A proud, big, haughty or stately look, stare, surliness, or surly look" and "A little gratel room wherein a new prisoner is set, and must continue some hours, that the Jailer's ordinary servants may the better take notice of his face."
Adopted as a general term in U.S., 1880s, replacing earlier dead house, etc. In newspaper slang, "collection of pre-written obituary material of living persons" (1903), hence "library of clips, photos, etc.," 1918.