As the title suggests, I'm curious about the origin of a "hung jury" when the jury doesn't come to a decision.
This column by Adam Freedman discusses the phrase:
The Oxford English Dictionary lists the first printed reference to a hung jury in Edwin Bryant’s What I Saw in California (1848-49) in which he states: “The jury . . . were what is called ‘hung’; they could not agree . . .”
Bryant’s phrasing obviously suggests that the phrase was already in common use by the late 1840’s. ... The earliest use of the term in a law report appears in an 1821 case, Evans v. McKinsey. ... it appears that the term developed somewhere in the south during the early 19th Century.
Linguistically, the phrase seems to derive from the sense of “hung” to mean caught, suspended or delayed (“I got hung up at the office”).
The Hung Jury: The American Jury's Insights and Contemporary Understanding [PDF] references the same cases, with a few more details (see footnote, pg 1).
The following clip from an 1838 issue of the Southern Literary Messenger confirms both the geography and time frame mentioned in @aedia's answer:
The OED's earliest citation is 1848, but I found an earlier example with the same meaning in Niles' Weekly Register of November 23, 1822:
Another meaning of hung is suspended, and the jury is figuratively suspended as it cannot make a decision.
A year earlier than Hugo's November 23, 1822, instance from Niles' Weekly Register is this very brief untitled item from the [Leesburg, Virginia] Genius of Liberty (August 28, 1821):
In Virginia, and in sundry other places nearer home, a jury that cannot agree, is called a hung jury. ...thus, when the jury are hung, the criminal is not!—[Fredonian.
The Fredonian cited as the source of this item is probably the New Brunswick, New Jersey Fredonian, a contemporaneous newspaper.
This instance establishes not only that, by August 1821, the term hung jury was in use in Virginia (and elsewhere) in the sense of "jury unable to reach a unanimous decision," but also that people were already making jokes that played on the double-entendre meaning of hung.