Numerous sources explain that "Fargo" was definitely not
a true story, but was very loosely based on two unrelated events from 1962 and 1972.
"Fargo opens with a title card proclaiming: "This is a true story. The events depicted in this film took place in Minnesota in 1987." Earnest journalists who went in search of the "real" woodchipper murders were outraged when, after months of wild goose chases and increasingly deadpan obfuscation by the film-makers, they finally admitted that the title card was actually an elaborate hoax - their way of "poking a hole in the true story balloon", according to William H Macy.
So Fargo was not, in fact, based on a true story. None of it really happened. There is no real "Jerry Lundegaard" out there."
http://www.guardian.co.uk/culture/2003/jun/06/artsfeatures1
"Fargo is a comedy-thriller about a wacky kidnapping scheme that goes incredibly wrong. The brothers originally said it was based on a true story, but a New York Post "investigation" got the brothers to admit the story actually popped out of their heads...If there's still any doubt, follow the credits through to the very end. You'll find the standard tiny-print disclaimer about "no resemblance to any persons living or dead . . ."
http://www.snopes.com/movies/films/fargo.asp
http://www.imdb.com/title/tt0116282/trivia