"mortuary," 1821, from French Morgue, originally a specific building in Paris where bodies were exposed for identification:
There is, in the most populous part of the French metropolis, an establishment entitled La Morgue, destined for the reception and exposition of bodies drowned in the Seine, and caught in nets, which are placed in different parts of the river for that purpose. The object of this exposition is, that the deceased may be recognised by their friends or relatives, and receive the rights of sepulture accordingly. The Morgue is open at all hours of the day, to passengers of every description, and often displays at a time, five or six horrible carcasses stretched, without covering, on an inclined platform, and subjected to the promiscuous gaze of the mob. ["American Review," January 1811]
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), thence extended generally to "library of clips, photos, etc." (1918).