Cops say Jimmy Snuka has been lying about what REALLY happened the day his GF died for DECADES ... and his own autobiography helped convince cops he's the murderer.
TMZ Sports has obtained documents from the grand jury that indicted the former WWF superstar ... which spells out why investigators believe he killed Nancy Argentino in 1983.
Long story short ... cops say Snuka told investigators in 1983 that Nancy injured her head while the two were "fooling around" outside of their motel room in Allentown, PA when he pushed her and she fell, striking her head.
Fast forward to 2012 ... when Snuka published his autobiography, "Superfly: The Jimmy Snuka Story" in which Jimmy's story changes RADICALLY.
In the book, Snuka says Nancy slipped and fell on her own while going to the bathroom at a rest stop. He makes no mention of an altercation whatsoever.
Well, cops took notice of the extreme change in his story and reopened the case -- ultimately, determining there was enough evidence to prove Snuka laid a serious beatdown on Nancy, which directly caused her death.
Snuka was arrested today in his NJ home. He has since posted bail.