Does a jury's failure to reach a verdict have any double jeopardy consequences? No: Yeager v United States  USSC No 08-67 (18 June 2009).
Failure to reach a verdict is a non-event. Strange to say, the New Zealand Court of Appeal dealt with the same point in R v Shaw  NZCA 232 (5 June 2009).
In Shaw there was one count, arson, but two ways in which the accused might have been liable: as a secondary party (arising from events some weeks before the fire) or as an offender at the scene; I refer to this latter as principal liability for simplicity - at the scene he could have been a secondary party, but the point of discussion here is the difference between liability at the scene and liability arising on a previous occasion. At the first trial, the jury convicted, and in answer to the Judge's (unusual) inquiry the foreman said this was on the basis of secondary liability. No information was sought or given about the jury's views on liability as a principal (they might have been unanimous or they might have been unable to agree, or they might not have decided the issue). The conviction was overturned on appeal because the accused had not been given sufficient notice of the Crown's intention to allege secondary liability. At retrial the judge directed the jury that they could convict even if they disagreed on the basis for liability. The jury convicted the accused and the judge did not inquire about the basis for that. One of the grounds of appeal was double jeopardy: the first jury should be taken to have decided that the accused did not commit the arson as a principal, so that could not be a basis for liability in the second trial. The majority on this point (Ellen France and Heath JJ) held that double jeopardy was not engaged: it would be wrong to infer that the jury had decided the issue of principal liability, let alone that they had rejected it. Principal liability was not addressed in the reason for verdict at the first trial. Nevertheless, a retrial was directed on the issue of secondary liability only: this was because Heath J was prepared to break the deadlock in this 3-judge bench by agreeing with the dissenter Fogarty J that, on broader abuse of process considerations, a real risk of double jeopardy was sufficient to prevent the prosecution from relying on liability as a principal, especially as it had always had the opportunity to allege the forms of liability as alternative counts in its indictment.
In Yeager the charges were, broadly, counts of fraudulently misleading the public about the virtues of an investment, insider trading by selling stock without disclosing to the public relevant information, and money laundering by dealing with the proceeds of the stock sales. The accused was acquitted on the fraud counts but the jury failed to reach agreement on the insider trading and money laundering counts. He was re-charged with some of the insider trading and money laundering counts. The Supreme Court had granted certiorari on the assumption that the Fifth Circuit had correctly ruled that the acquittals on the fraud counts meant that the jury had decided the accused did not have the information necessary for conviction on the insider trading charges. In fact the Fifth Circuit had reasoned that the failure to reach verdicts meant that the jury had not decided that the accused had the insider information, so the Supreme Court left open the opportunity for the Fifth Circuit to revisit its factual analysis of what, on the evidence, the acquittals necessarily meant: had the jury necessarily decided that the accused did not have the information that he was alleged to have had and which it was necessary to prove he had if he were to be convicted on the insider trading and money laundering counts?
The double jeopardy focus was thus on the meaning of the acquittals, not on the meaning of the failures to reach verdicts. "No verdict" has no meaning. Stevens J, delivering the opinion of the Court, put it like this: "the consideration of hung counts has no place in the issue-preclusion analysis."
Yeager decides that acquittals can have double jeopardy implications for counts on which no verdict has been reached (even by the same jury). Scalia J dissented on the basis - I summarise - that as the proceedings on the hung counts were not concluded they were the same proceedings as had involved the acquittals, so the acquittals were not prior in the double jeopardy sense. Alito J, also dissenting, noted that in this situation "the conclusion that the not-guilty verdicts preclude retrial on the hung counts necessarily means that the jury did not act rationally." That is because the jury must have been in doubt about a fact essential for conviction on the hung count (for double jeopardy to apply), and should have acquitted on both. He stressed that a strict analysis is necessary, as Ashe v. Swenson, 397 U. S. 436 (1970)
"made it clear that an acquittal on one charge precludes a subsequent trial on a different charge only if "a rational jury" could not have acquitted on the first charge without finding in the defendant's favor on a factual issue that the prosecution would have to prove in order to convict in the later trial. Id., at 444. This is a demanding standard."
Stevens J did not disagree on this:
"The reasoning in Ashe is ... controlling because, for double jeopardy purposes, the jury's inability to reach a verdict on the insider trading counts was a nonevent and the acquittals on the fraud counts are entitled to the same effect as Ashe's acquittal."