Green’s Dictionary of Slang

hang it on v.1

[the image is of hanging something on a peg and forgetting it]

1. to protract, to put into abeyance.

[Aus]Vaux Vocab. of the Flash Lang. in McLachlan (1964) 245: hang it on purposely to delay or protract the performance of any task or service you have undertaken, by dallying, and making as slow a progress as possible, either from natural indolence, or to answer some private end of your own.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue [as cit. 1812].

2. to cohabit with a woman, to form a temporary sexual relationship.

[Aus]Vaux Vocab. of the Flash Lang. in McLachlan (1964) 245: To hang it on with a woman, is to form a temporary connexion with her; to cohabit or keep company with her without marriage.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue [as cit. 1812].

3. (US und.) to carry out some form of swindle or extortion.

[US]F. Hutchison Philosophy of Johnny the Gent 85: ‘She must be a bear wit’ that stingin' spiel! [...] they tell me she hung it on a lot o' them main guys in a bank, an other supposed-to-be wise gazabos fer about a million!’.

SE in slang uses

In phrases

hang it on the limb (v.) (also hang it on a bush) [ety. unknown; ? image of a member of a work gang removing his prison uniform and hanging it from a tree or bush before running]

(US prison) to escape from prison or from a chain gang.

[UK](con. 1922) R.E. Burns I Am a Fugitive 69: Sam, I got six years; that’s a long time, and I’m going to try to ‘hang it on the limb’, and I need a little help. [Ibid.] 80: He just hung six years on the limb, and ain’t seen a girl for the last three months.
[US] in Western Folklore XIV (1955) 135: Hanging it on a bush. To escape from prison.
[US]G. Duffy Warden’s Wife 146: For nearly a year...no convict had succeeded in ‘hanging it on a bush’ .