I would guess this phrase would go back as far as people were tried for murder. It has a very literal meaning, and probably wouldn't have taken any overly wise or insightful person to use this in another context.
(idiomatic) To do something bad or illegal and not be punished. quotations:
1984:"He'd spoil the boy just as we have all spoiled him, and though he's a big strapping fellow and a soldier at that, he'd let Ned get away with murder just as I've done." — James Purdy (1984). On Glory's Course, 147, Viking Press. ISBN 0670524514.
2000:"It's because you let people get away with murder, Quill." — Claudia Bishop (2000). Marinade for Murder. Berkley. ISBN 0425176118.
1980:"Just yesterday it was fashionable to be black. Remember? Any black writer could get away with murder, just as any Jewish-American writer can get away with murder." — Gore Vidal and Robert J. Stanton (1980). Views from a Window: Conversations with Gore Vidal, 245, L. Stuart. ISBN 0818403020.
2005:"He said I found out about everything he did and said, 'I can't get away with nothing, and Jim can get away with murder.' I don't think that I let any of my kids get away with murder, and I don't think any one of them ever did much serious mischief." — James M. Hill, Sr. (2005). I Have Been Blessed!: Hard Work and Happiness, 205, Aforesight Press. ISBN 0977485994.
Is far as I remember it has to do with being murder the ultimate crime, one of the seven deadly sins.
If you get away with murder you can get away with anything.