The hearing is being held before Justice Maxwell Wiley in State Supreme Court in Manhattan to determine if Mr. Hernandez’s statements to the police and prosecutors can be admitted as evidence at trial.

A central question Justice Wiley must answer is whether Mr. Hernandez was at the Camden County prosecutor’s office in New Jersey voluntarily, or because he was in custody. Once a suspect is in custody, the law requires the police to inform suspects of their right to remain silent and to have an attorney present.

Mr. Hernandez, 53, of Maple Shade, N.J., has an I.Q. of about 70 and a history of mental illness. The lead defense lawyer, Harvey Fishbein, has argued in court papers that Mr. Hernandez not only believed he was under arrest but also could not understand his rights well enough to waive them. Mr. Fishbein has also argued Mr. Hernandez is so suggestible and compliant that he gave the police a false confession.

That confession came after more than six hours of interrogation during which Mr. Hernandez had twice asked to go home, according to testimony at the hearing.

Mr. Hernandez’s statement to the three detectives, as well as a second statement given 11 hours later to a prosecutor in New York, are critical to the Manhattan district attorney’s case. No other evidence has been made public that links Mr. Hernandez to Etan’s disappearance on May 25, 1979.