LOS ANGELES (AP) _ The defense and prosecution rested their cases Monday in the murder trial of obsessed fan Robert Bardo in the killing of actress Rebecca Schaeffer. The judge said he may deliver a verdict Tuesday after he hears closing arguments.

Superior Court Judge Dino Fulgoni is hearing the case without a jury. The prosecution agreed not to seek the death penalty after Bardo agreed to waive trial by jury.

Bardo, the fan who pursued the 21-year-old star of ''My Sister Sam'' for two years, has admitted shooting her to death July 18, 1989, at the front door of her apartment building.

Bardo's lawyer, Deputy Public Defender Stephen Galindo, has presented psychiatric evidence in an effort to show Bardo was not in his right mind and didn't intend to kill Miss Schaeffer until he was at her door.

Bardo, 21, of Tucson, Ariz., has been diagnosed as schizophrenic but a psychiatrist testified he wasn't legally insane at the time of the killing.

Bardo told the psychiatrist he shot on impulse because Miss Schaeffer was arrogant and told him to go away. The prosecutor claims Bardo premeditated the killing after lying in wait for the actress.

Fulgoni must decide whether to convict Bardo of first-degree murder and the special circumstance of lying in wait. If convicted of both, Bardo would face life imprisonment without parole. A simple first-degree conviction would allow a sentence of 25 years to life with parole possible.

One crucial question for the judge as he rules on the lying-in-wait issue is whether Bardo and Miss Schaeffer talked before the shooting.

In tests conductd Friday, public defender's investigator Rommel Agee and lawyers for both sides went to the apartment house and re-enacted the shooting to determine whether a neighbor could have overheard conversation between Miss Schaeffer and Bardo.

Agee testified he stood where witness Lynn Marta said she was standing in her apartment at the time of the shooting. With Deputy District Attorney Marcia Clark taking the role of Miss Schaeffer, Agee said he could hear the doorbell, Miss Clark's footsteps coming down the hall and the front door opening. But he said a man's voice speaking outside the door was indistinct.

''I could not make out what was being said,'' he testified.

Ms. Marta had testified for the prosecution that she heard no one talking before the shots were fired. Agee, although testifying for the defense, corroborated her statement.