NY- The father of a 21-year-old aspiring dancer flew to New York last night to claim her body, apparently unaware the brunette beauty had been performing on Broadway – at a topless club under the name Ava.

“She was realizing her dream and she was very excited about it,” said Catherine Woods’ devastated dad, Jon Woods, as he left Columbus, where he is director of the Ohio State University Marching Band.

“She really met the challenge of moving to New York. It took amazing courage.”

Her hometown boyfriend, David Haughn, told cops he found Woods – nearly decapitated, with her larynx and jugular vein severed – in the blood-soaked bathroom of their E. 86th St. apartment Sunday night.

Police sources said investigators, for now, are accepting Haughn’s alibi that he was fetching his car to drive Woods to a strip joint when she was slain.

“We haven’t been able to shake his story,” one source said. “He didn’t appear to have the time to do the things that we know have happened, and check out and not have blood on him.”

Haughn was still at the 19th Precinct stationhouse last night, where he has been ever since Woods’ body was found. An aspiring hip-hop musician from Columbus who worked as a doorman at an upper East Side building, Haughn told cops that Woods had been threatened by a man for failing to return some borrowed CDs.

Sources said Woods had broken up with Haughn and had found a new boyfriend, who also has been questioned by police. Barry Lisbon, manager of Flash Dancers on Broadway at 52nd St., said Woods was scheduled to dance at the club on Sunday night.

“We knew her as Ava,” he said. “She was very wholesome. We don’t know what world outside of here she lived in.”

Woods had told her parents she performed in a play called “The Privileged.” That’s also the name on a private room in a Chelsea gentlemen’s club called Privilege, where Woods performed from April through July.

“I’m assuming . . . that she didn’t want her folks to know what she was doing,” said manager Anthony Regina.

Woods was a Midwestern girl, the eldest of three children, who inherited her father’s musical talent. She started dancing at age 3 and was barely out of high school when she left for the bright lights of Broadway.

“She always wanted to go for broke in dance,” Jon Woods said. “There were other opportunities, but she only wanted to go to New York City.”

Some Ohio State pals of the family helped Catherine find her first apartment on E. 85th St. Her dad said he was thrilled because he figured it was a safe area.

“When she first got there, she landed a job in a dance troupe,” Jon Woods said.

And in weekly calls home, Woods told her parents how she traveled up and down the East Coast performing at colleges, and how she nearly made the cut as a dancer in the Broadway show “Sweet Charity.”

A dancer at Flash Dancers said Woods would often talk of her family and her struggles to find work on Broadway during cigarette breaks.

“She’d only been here four months. She was a professional dancer. She came to New York to find theater work,” said the dancer, who identified herself only as Melanie.

“She was a sweet, nice girl. She missed her family a lot. She was eventually going to go back to them. . . . It’s just awful.”

Jon Woods said he visited his daughter several times when she was down about small traumas he described as “nothing major.” He said little about Haughn, 23.

Ken Szymanski, who was a neighbor of Woods and Haughn when they lived on E. 85th St., said they were “very nice, very mellow people” who often jogged together around the Central Park reservoir.

“They seemed kind to each other,” Szymanski said.

But something changed in their relationship after they moved to E. 86th St.

Antonio Ramirez, who manages Gracie’s Corner Diner at First Ave. and 86th St., said Woods came in just about every day and always ordered a spinach egg-white omelet. But a month ago, Ramirez said, “She came in by herself and I said, ‘How’s your boyfriend?’

“She said, ‘He’s not my boyfriend anymore. I broke it off,’ ” Ramirez said.

“She said they were only good friends,” he added.

Jon Woods said he plans to bury his daughter after a funeral Friday.

“She was a natural dancer who flowed with the music,” he said. “I hope they get the right person.”