To the surprise of Suffolk homicide detectives, a Brooklyn woman they were investigating in the death and dismemberment of her neighbor showed up at a precinct house and asked to speak to them, detectives testified Monday.

When Leah Cuevas, 44, went to the 73rd Precinct in Brooklyn on the evening of July 11, 2014, not all of Chinelle Latoya Thompson Browne, 28, had been found yet. By then, detectives had found her torso and legs in Bay Shore and her arms in Hempstead. The discovery of her head, also in Hempstead, was still six days away.

But Cuevas knew Browne was missing and that Suffolk police had searched Cuevas’ apartment, so she wanted to explain herself, Dets. Michael Mahan and Angel Rivera testified in Riverhead. Cuevas is on trial before Suffolk County Court Judge John Toomey Jr., charged with second-degree murder.

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Cuevas said she and Browne, her former friend, had argued bitterly and fought physically during a dispute over whether Browne owed Cuevas rent, as well as the two women’s relative sexual morality. Defense attorney Mary Elizabeth Abbate has said the fight happened, but her client did not kill Browne.

Cuevas said she last saw Browne the morning of July 7, leaving the building they lived in with some of her belongings, Mahan said. Shortly afterward, he said he told Cuevas that Browne was dead and that police were reviewing surveillance video in the area.

“She’s dead? Are you saying I killed her?” Cuevas said, according to Mahan. “Did you see me carrying a body out? Did you see me carrying bags? I don’t kill people, understand me. I can’t do that.”

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Cuevas is accused of stabbing Browne to death on July 5, cutting her into pieces and stuffing them into a suitcase before taking a cab to Long Island to dump them.

Mahan said he thanked her for coming forward and let her go. The investigation continued, and police gathered more evidence until July 23. On that day, he said, he arrested Cuevas after she left her sister’s home in Bay Shore.

“I didn’t kill her,” Cuevas said after she was handcuffed, according to Mahan. “People who live like her get what they get.”

That appeared to be a reference to what Cuevas told detectives earlier that month at the Brooklyn precinct. Then, she told detectives that Cuevas had been renting an upstairs apartment from her for $400 a month, until squatters in the building convinced her that Cuevas was not the rightful owner.

Cuevas acknowledged a dispute between her and the daughter of the previous owner, who had died, over the ownership.

The rent dispute was in addition to what Cuevas said was Browne’s objectionable lifestyle.

“She said Chinelle has been living a double life, sleeping with a lot of men,” Rivera testified.

The dispute boiled over July 5 when Cuevas said she and Browne argued about rent and utility payment and about whether both women were cheating on their husbands. Then they started punching each other, she said according to Rivera.

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“I hit her a lot,” Cuevas said, according to Rivera. “I said, ‘Chinelle, you’re fighting the wrong person.’ I hit her hard. I used to do tae kwon do.”

But she said the fight ended with Browne alive and leaving with a friend while Cuevas taunted her, Rivera said.