Set in Washington DC, Suspect centers on three disparate characters. Carl Wayne Anderson is a homeless, deaf-mute Vietnam veteran accused of murdering Elizabeth Quinn, a file clerk at the Justice Department. Kathleen Riley is the beleaguered Federal Public Defender assigned to represent Anderson. An agribusiness lobbyist who normally works on Capitol Hill, Eddie Sanger, is made a member of the jury and begins investigating the details of the murder himself, eventually teaming up with Riley to solve the case. We see some early scenes of Sanger's work as a lobbyist on Capitol Hill, including his efforts to win passage of a bill by seducing a Congresswoman. While not relevant to the movie's plot, these scenes are establishing shots giving us a sense for Sanger as a charming, though somewhat ruthless, person.
The movie begins around Christmas with the suicide of a United States Supreme Court Justice, for which no explanation or context is given. We only see the Justice making a tape recording and then shooting himself. Shortly after the Justice's suicide, Elizabeth Quinn's body is found floating in the Potomac river, and Carl Wayne Anderson is arrested for the crime, based almost entirely on the fact that he was found sleeping in Quinn's car, which was abandoned in the parking lot where she worked (and was mostly deserted at night). Anderson explains that he found it 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 found in Quinn's car, he was arrested for her murder. The establishing scenes show Riley trying to communicate with Anderson and realizing that he is 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.
In the District of Columbia, all crimes are tried in the federal courts, so a murder trial that would normally be in state court was in federal court instead. Riley selects Sanger to be a member of her jury. Soon thereafter, it becomes clear that Sanger is intent on helping Riley with her investigation and defense of Anderson. As the investigation by Riley and Sanger intensifies, they begin focusing on Deputy Attorney General Paul Gray. Figuring that a key found on Elizabeth Quinn'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 that it unlocks a file cabinet, which contained trial transcripts from federal cases from 1968 that Quinn was in the process of transcribing.
While the investigation goes on after hours, the movie shows scenes during the day from Anderson's murder trial. During the trial, we are introduced to the stern federal 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. One key sequence in a law library (where Riley and Sanger continue looking for the elusive case from 1968 that may be the key to the murder) brings Helms, Riley and Sanger into close proximity. Riley and Sanger narrowly avoid being caught by Judge Helms. Eventually, Judge Helms sequesters the jury to avoid further contact between Riley and Sanger.
Riley and Sanger continue tracking the federal court cases from 1968. Their theory is that Elizabeth Quinn stumbled onto something during her transcription of those cases. They look for any case that might have an impropriety. As is explained to the audience, fixing a case requires participation from both the prosecutor and the trial judge. Riley and Sanger think they will find evidence that Paul Gray was a prosecutor on a rigged 1968 case, which would be his motive to murder Elizabeth Quinn if she approached Gray about what she found. Eventually, 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 we saw the Supreme Court Justice making at the beginning of the movie. 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. Riley assumes the prosecutor on that case was Paul Gray and goes back to the courthouse to retrieve the case book that will confirm this. As she gets to the courthouse (now deserted at night), 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 was able to slice the right wrist of her assailant, who then fled unseen.
The following day takes place in court. Paul Gray shows up in the courtroom, to the surprise of Judge Helms. Riley then tells Judge Helms that she wants him to take the stand. Irate and perplexed, Helms says that Riley cannot make him testify as he is the presiding judge. Then, in a somewhat-rushed speech, Riley reveals that Judge Helms, not Paul Gray, was the prosecutor in the fixed case in 1968. The Supreme Court Justice was the presiding judge in that case. In exchange for fixing the case, he was promoted from the District Court to the Court of Appeals. Helms, who was the prosecutor on the fixed case, was appointed to the District Court. Judge Helms then waited 17 years (from 1969 to 1986) to be promoted again to the Court of Appeals. Just as he learned he was the President's nominee, Quinn inadvertently discovered the case fixing as she transcribed the cases from 1968. She approached the Supreme Court Justice, who responded by committing suicide. By contrast, when she approached Judge Helms, he murdered her. As Judge Helms 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.
The movie ends with Riley reinvigorated in her job and in a relationship with Sanger.