Suspect

Around Christmas, a United States Supreme Court Justice commits suicide, for which no explanation or context is given. We only see the Justice making a tape recording and then shooting himself. Shortly after the suicide, the body of Elizabeth Quinn, a file clerk at the Justice Department, is found floating in the Potomac River, and Carl Wayne Anderson (Liam Neeson), a homeless, deaf-mute Vietnam veteran, is arrested for the crime, based almost entirely on the fact that he was seen sleeping in Quinn's car the night of her murder. Kathleen Riley (Cher) is the beleaguered D.C. public defender assigned to represent Anderson.
The car was abandoned in a desolate K Street parking lot. Anderson, it is eventually revealed, found the car unlocked and was just looking for a warm place to sleep since it was the dead of winter. But since he was homeless, had no alibi, and was also found in possession of Quinn's wallet, he was arrested for her murder.
Riley finds it difficult to communicate with Anderson, a deaf-mute. Over time, she begins to penetrate his hard exterior and he tries to cooperate with her efforts to mount a defense for him.
An agribusiness lobbyist who normally works on Capitol Hill, Eddie Sanger (Dennis Quaid), is approved as a member of the jury by Riley despite his attempt to be excused. Sanger begins investigating the details of the murder himself, eventually teaming up with Riley beyond the observation of the trial's suspicious judge.
Sanger also keeps busy in his work as a lobbyist on Capitol Hill, including his efforts to win passage of a bill by seducing a Congresswoman.
As the investigation by Riley, with unethical assistance from Sanger, intensifies, they begin focusing on Deputy Attorney General Paul Gray (Philip Bosco). Figuring that a key found on the victim's body has something to do with the Justice Department (where Quinn worked), Riley and Sanger break into the file department at the Justice Department late one night and try to find what the key unlocks. They find a file cabinet, which contained trial transcripts from federal cases from 1968 that Quinn was in the process of transcribing.
The trial is conducted by stern judge Matthew Helms (John Mahoney). Helms is rumored to be the President's nominee for a seat on the prestigious United States Court of Appeals for the District of Columbia. Judge Helms begins to suspect that Riley may be collaborating with Sanger, which would be a disbarrable offense of jury tampering, although he does not have concrete proof.
In a law library, Riley and Sanger narrowly avoid being caught by Judge Helms, who sequesters the jury to avoid any possible further contact between Riley and the juror.
Riley and Sanger suspect that Elizabeth Quinn stumbled onto something and look for any case that might have an impropriety. Fixing a case requires participation from both the prosecutor and the trial judge. Riley and Sanger think they will find evidence that Gray was the prosecutor on a rigged 1968 case, which would be his motive to murder Quinn if she approached Gray about what she found.
Riley goes back to Quinn's car (still impounded where it was found in a government parking lot) and finds an audiotape that the police did not uncover in their half-hearted investigation. The tape is the one made by the Supreme Court Justice who committed suicide. In it, he confesses to conspiring to fix a case in 1968 (with a politically influential defendant) in return for an appointment from the United States District Court to the United States Court of Appeals for the District of Columbia Circuit.
Riley assumes the prosecutor on that case was Gray and goes back to the courthouse to retrieve the case book that will confirm this. She is pursued and attacked by an unseen figure. With the help of Sanger (who managed to get away from being sequestered by creating a diversion with a fire alarm), Riley is able to slice the right wrist of her assailant, who then flees unseen.
Gray shows up in the courtroom, to the surprise of Judge Helms. Riley wants the judge to take the stand. An irate Helms says that Riley cannot make him testify. Riley reveals that it was Helms, not Gray, who was the prosecutor in the fixed case of 1968. In exchange for fixing the case, Helms was nominated to the District Court.
Seventeen years later, Quinn inadvertently discovered the case fixing. At the same time, Helms learned he was a likely nominee for the Court of Appeals. Quinn approached the Supreme Court Justice, who responded by committing suicide. When she approached Judge Helms, however, he murdered her. As the judge angrily bangs his gavel during Riley's accusation, his right wrist begins to bleed from where Riley slashed him the night before, confirming his identity as the killer.
Riley ends up reinvigorated in her job and in a relationship with Sanger.

Question: Riley goes back to the courthouse for what?
Answer: Riley goes back to the courthouse to retrieve a case book.