BROCKTON — Keith Luke, the 26-year-old Brockton man accused of killing two people and raping and shooting a third person, should not be held criminally responsible because he is mentally ill and suffers from paranoid schizophrenia, his defense attorney said today.

“He becomes paranoid that people are out to get him, he’s staying up all night walking around the house, changes his sleep patterns, terrified to sleep at night, tells his mother to stay away from windows,” attorney Joseph Krowski Jr. said in closing arguments in Luke’s Plymouth County Superior Court trial. “He sleeps on a crucifix made of cinder blocks.”

Prosecutor Frank Middleton countered by saying that Luke’s action were cold and calculated and that the defendant never exhibited any signs of being mentally ill prior to, during, and after his killing spree.

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“There was no ranting and raving, no bizarre thoughts,” Middleton told jurors of Luke’s demeanor two hours after his arrest, referring to a taped interview the defendant had with police, a video that jurors viewed during the two-week trial.

The jury is now deliberating in the case. Luke is on trial for the Jan. 21, 2009, fatal shooting of Selma Goncalves, 20, and Arlindo DePina Goncalves, 79, who were not related. Luke is also accused of raping and shooting Selma Goncalves’s 22-year-old sister.

The sister survived. The Globe is not identifying her because she is the victim of an alleged sexual assault. She sat in the courtroom next to her father during the closing arguments, both with grim expressions on their faces.

She testified during the two-week trial, saying she expected to see a friend when she opened her apartment door and encountered Luke that horrifying afternoon.