A conviction based on evidence obtained through torture is a violation of not only the common law inherited from England and the U.S. Constitution, but also a United Nations treaty. (The U.S. is a signatory to the Convention Against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment.)
Generally, the admissibility of statements and other evidence allegedly obtained through torture turns on the question of whether the statement was voluntary; voluntariness is a matter for a judge to determine before trial. In certain types of proceedings, however, a judge may admit a statement or the evidence derived from it even if it was involuntary due to torture. (For more on this topic, see Miranda and Involuntary Confessions. Also see Nolo's pages on Police Misconduct and Police Brutality.)
Typically, a lawyer whose client may have been tortured into giving statements files a motion to suppress evidence. In the motion, the lawyer lays out the facts and law, asserting that the statements and any evidence they led to are inadmissible.
The prosecution then has the burden of proving that the statements in question were actually voluntary. The prosecution can do this by showing either that the claims of torture aren’t credible or that any torture that did happen didn’t produce the statements. The judge must then determine, outside the presence of the jury, whether the statements were voluntary.
Even if the judge determines the statements or the evidence they led to are admissible, the defense can probably present evidence regarding the alleged torture to the jury. The judge will typically instruct the jury that it may disregard the defendant’s statements if it believes them to be based on torture or the threat thereof; the jury may choose to ignore the statement or the evidence derived from it. But, as defense lawyers often say, you can’t “unring a bell”—it’s difficult for jurors to ignore a confession they’ve already heard, no matter how the government came by it.
Normally, a defendant doesn’t have “standing” to complain about the violation of someone else’s rights. But courts consider torture so repugnant that they may suppress a torture-produced statement by someone other than the defendant. If, for example, a codefendant confessed under torture to the defendant’s involvement in a crime, the defendant could move to suppress the codefendant’s statement.
Some cases have held that the “exclusionary rule”—the rule that prevents admission of evidence obtained in violation of constitutional rights—may not apply in certain cases. Depending on the facts, statements procured through torture may be admissible in proceedings like extradition and detention hearings relating to matters of national security.
Courts often find government agents highly credible; they may be predisposed to reject a defendant’s claims of torture. An experienced attorney will be well-versed in the nuances of the applicable law and, if the facts oblige, capable of presenting a case that the client’s statements were involuntary. If you have been tortured or even threatened by law enforcement, immediately consult a lawyer.