"hard aromatic seed of the fruit of a tree found in the East Indies," used as a spice on cookery, c. 1300, note-mug, from Old North French or Anglo-French *noiz mugue, from Old French nois muguete, an unexplained alteration of nois muscade "nut smelling like musk," from nois "nut" (from Latin nux, from PIE *kneu- "nut;" see nucleus) + Latin muscada, fem. of muscat "musky" (see muscat). Probably influenced in English by Medieval Latin nux maga (compare unaltered Dutch muskaatnoot, German muscatnuß, Swedish muskotnöt).
American English colloquial wooden nutmeg "anything false or fraudulent" is from 1827; Connecticut is called the Nutmeg State "in allusion to the story that wooden nutmegs are there manufactured for exportation." [John Russell Bartlett, "Dictionary of Americanisms," 1859]
At a dinner party, the other day, during a little playful discussion of Yankee character, a bland and benevolent-looking old gentleman at my side informed me that he had come to the conclusion that the wooden-nutmeg story was neither more nor less than a mischievous satire. "For," said he, "there would be such an amount of minute carving required to make a successful imitation of the nutmeg, that the deception would hardly pay the workman. For myself, I do not believe the cheat was ever practised." I thanked him in the name of my country for the justice done her, and assured him that the story of the Yankee having whittled a large lot of unsaleable shoe-pegs into melon seeds, and sold them to the Canadians, was also a base fabrication of our enemies. [Grace Greenwood, "Haps and Mishaps of a Tour in Europe in 1853"]