His long hair flowing behind him, Paul Cortez strolled the mirrored workout rooms inside the Equinox gym on E. 85th St. with a calmness that did not go unnoticed.

"He is very mellow, very soft, very sexual," said Wendy Marquez, 31, a former colleague of Cortez's. "He has something that attracts women - something very calm."

On that day, Catherine Woods, a 21-year-old stripper from Ohio, was viciously stabbed to death inside the cramped studio apartment she shared on the upper East Side with her ex-boyfriend, David Haughn.

Cops quickly zeroed in on Haughn, 23, an aspiring rapper, as the prime suspect in the ghastly murder. His relationship with Woods had soured since the longtime flames moved to New York City from Columbus, Ohio, in 2001.

The young beauty fell for the charming, long-haired lothario, who, according to friends and co-workers, had little trouble scoring dates. But there was another side to Cortez that he tried to hide from Woods. He was an insatiable flirt, prone to pursuing women aggressively.

The love affair between Cortez and Woods appeared to heat up quickly. They were spotted several times engaging in steamy makeout sessions in secluded parts of the gym.

Woods' family and many of her friends had no idea she had been earning money as a topless dancer. They had been told the aspiring Broadway performer was making ends meet by working at a restaurant and teaching dance classes.

Not long after Cortez and Woods began seeing each other, she apparently got bored with him and broke it off. And just as he had in the past with other attractive women, Cortez took the news hard.

"When they broke up, he was talking to his clients about it," said a 31-year-old woman who works out at Equinox. "He wasn't taking it well at all."

On the evening of Nov. 27, Woods was chatting away on the phone with her best friend as she got ready for her shift at a topless club near Times Square.

Haughn, her loyal ex-boyfriend, who often drove her to work, left the apartment to fetch his car. When he returned 20 minutes later, he found her lifeless body in a pool of blood.

Cops held Haughn for several hours after the attack. But he cooperated with investigators, answering their questions, giving them fingerprints and DNA samples. He was released.

Days later, investigators shifted their focus to Cortez. He soon became the prime suspect, but cops did not have enough evidence to bust him, even though a surveillance camera appeared to catch him lurking around Woods' apartment before the murder. Cops said he also called Woods seven times from his cell phone before her slaying.

Police got a break last week when another woman came forward and accused Cortez of raping her last New Year's Day. He was busted late Monday on the sex charge, allowing cops to fingerprint him.

Police then matched his prints to one found near Woods' body. Cortez was indicted Friday for her murder. Speaking in a soft voice, he pleaded not guilty.

"It tickled me to death when I found out they caught him," said Haughn's grandmother, Anita Gaston, who lives in Columbus. "It's a huge load off of all of us."

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