The evidence against a Mastic man charged with a gruesome rape and murder of a Medford woman is so overwhelming there should be no question he did it, a Suffolk prosecutor told a jury Wednesday.

But the defense for Dante Taylor, 20, told jurors much of that evidence is fraudulent and the prosecution illegally withheld evidence pointing to other suspects who might have stabbed Sarah Goode, 21, more than two dozen times in the head and numerous times in the chest and legs.

The opening statements by Assistant District Attorney Janet Albertson and defense attorney John Lewis Jr. of Farmingdale were delivered to a full courtroom before state Supreme Court Justice John Collins in Riverhead. Albertson’s statement was interrupted when a juror passed out, but after an hour and some food, he recovered.

Goode was killed after 1 a.m. on June 7, 2014, Albertson said, hours after the victim’s close friend, Jason Flores, introduced her to Taylor — recently discharged from the Marines — at a party in Mastic. She dropped off Flores at his home and texted him she was home.

Almost right away, however, Albertson said Goode was on the phone with Taylor.

“The evidence will indicate this young lady made a very, very, very foolish decision,” Albertson said. “It was not only foolish, it was fatal.”

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The next morning, her BMW was spotted parked near some woods. A police officer looked at it briefly, but noticed nothing amiss, Albertson said. But when he saw it again the next day he saw a clump of hair sticking out of the doorjamb, blood on the outside of the car, blood all over the inside and what appeared to be a handprint left in blood on the hood, she said.

The blood was Goode’s. The palm print was Taylor’s, Albertson said.

After Goode’s decomposing body was found on June 12 about a mile from where her car was left, an autopsy found Taylor’s semen in her.

“Clearly, he wanted something from her that she did not want to give up,” Albertson said.

When investigators examined Taylor’s car about a month later, they found a small bloodstain that matched Goode’s DNA, Albertson said. “One bloodstain from a dead girl is one too many,” she said.

In his opening statement, Lewis asked why investigators searched that car thoroughly twice before without finding the blood. He suggested it wasn’t there the first two times. He also asked why investigators took no close-up photograph of the palm print and suggested it wasn’t actually in blood.

He conceded that his client had consensual sex with Goode and questioned whether she was raped. He noted that the autopsy found none of the genital injuries common in violent sexual assaults.

Lewis told jurors about a host of law enforcement missteps that he says both violated his client’s rights and kept police from pursuing other possible suspects. Before police focused on Taylor, he said, they roughed up Flores.

Police first arrested his client illegally on June 10, he said. Not only did they find no blood in his car that day, they also saw no marks on his hands or face indicating he had been in a violent struggle just days before.

Lewis said police ignored the fact that Goode had broken up with her boyfriend two days before she was attacked and that he didn’t come into work the day she disappeared. He did, however, leave a threatening voicemail message on her phone — a message police destroyed and didn’t disclose to the defense for more than a year.

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Collins earlier in the case had ruled that the June 10 arrest and search was illegal and should be suppressed. But Lewis said he wanted jurors to know about that, in conjunction with other law enforcement missteps, so that jurors had a full understanding of police ineptitude and improper behavior in the case.

Goode, who had a young daughter, was the youngest of nine — and many of her family were in the courtroom Wednesday.

“We just want justice for our sister, and we’re finally on the road to get it,” said one sister, Elizabeth DeMuria.