In many states, when prosecutors initiate a case through the use of a grand jury, they must present evidence that's helpful to the accused. This duty doesn't require that they present every piece of favorable evidence—they generally only have to offer evidence that strongly points to innocence. But in other states and in federal court, prosecutors have no duty at all to present evidence helpful to the accused.
A grand jury is a panel of citizens called for service just like a trial jury (also called a "petit jury") in a criminal or civil case. But a grand jury's function is different from that of a trial jury.
A trial jury decides issues of guilt after the case has been through trial. A grand jury, on the other hand, hears a prosecutor's evidence that the accused probably committed a crime. At this point, the prosecutor hasn't even charged the suspect. If the grand jury decides that the accused probably committed a crime, then it will issue an indictment, effectively bringing criminal charges against the accused.
Prosecutors present evidence of criminal activity in an attempt to convince the grand jury that criminal charges are warranted. In some states and in federal court, they don't have to present any evidence suggesting that the target is innocent. The rationale is that the defendant will have the opportunity to present this evidence at trial.
For example, if prosecutors are seeking an indictment of Jane for an armed robbery, they might offer evidence of her fingerprints at the crime scene and a suitcase of money found in her car. In some states and in federal court, they wouldn't have to tell the grand jury that she has an alibi for the robbery.
In most states, prosecutors can't present half-truths to grand juries. If prosecutors have strong, credible evidence that points to innocence, they must divulge it. That doesn't mean, however, that they have to offer every piece of evidence that's helpful to the accused or that might be used at trial by the defense.
For example, evidence that a prosecution witness is a habitual liar would be helpful to the defendant at trial, but it doesn't directly negate the commission of the crime. Therefore, a prosecutor wouldn't be required to present it to a grand jury. And even in states where prosecutors have to present evidence of innocence, they don't have to go looking for it. In the example above, they would have to present Jane's alibi only if they were aware of it—they wouldn't have to try to find out whether she had one.
Even if a prosecutor ignores the duty to offer evidence of innocence, the defendant may be out of luck. That's because grand jury proceedings are secret, so it's difficult to know what was or was not presented to the jurors. Courts may release the grand jury records if the defense has made a really strong case as to why the information is necessary, but they don't often grant these requests. And the defense must bring any motion trying to overturn the indictment before trial; otherwise, the court won't consider it.