When this sultry brunette gave cops a topless tour of her Lower East Side photo exhibit, they were so smitten they declined to shut it down, even though neighbors had complained that pictures of her masturbating were in the window.

Police showed up yesterday afternoon at the ROX Gallery and met 24-year-old beauty Natalie White — who went bare-breasted as she showed them the exhibit, which is plastered with explicit photos of her. She even invited them to last night’s opening.

The cops were so taken, they declined to shutter the show — which includes pictures by photographer Peter Beard of White pleasuring herself.

“We met the police. They said they would come tonight,” said White who is known on occasion to masturbate live in front of gallery patrons.

“They came in full force,” she said. “It was like a moment out of ‘The Big Lebowski.’ ”

White’s attorney, First Amendment lawyer Ron Kuby, was less amused by the cops’ investigation.

“Why did they feel it was necessary to come inside and meet the naked girl?” Kuby asked.

“Maybe they’re just being thorough, leaving no stone unturned.”

White, once an unknown ingenue from West Virginia, became famous at the age of 17 when she met 75-year-old artist Beard at Bungalow 8 in Chelsea.

She traveled around the world with the lensman, acting as his muse. The two were openly having an affair while Beard was married to his wife and art dealer Nejma.

“Like Aphrodite, born from the sea, Natalie continually re-emerged as a muse of over 20 other artists,” ROX Gallery owner Emerald Fitzgerald said of the exhibit, called “Who Shot Natalie White?” — which features naked photographs of White by 25 different artists, including Beard, Spencer Tunick, Michael Dweck, Olivier Zahm and Sean Lennon.

“I would imagine that a lot of people did [complain],” White said of the racy photos, which are plastered in windows facing busy Delancey Street.

“For some reason, they’re so conservative in the US,” she said.

“It’s not masturbation — it’s just making love to myself in the photographs.”

Last night’s opening was marred by a fight between a former employee and a bouncer that prompted a call to cops, who arrived just as the event ended.

Curator Gregory de la Haba suspects that elderly Lower East Side residents called the police. “One walked in from the street and said, ‘Take this pornography down!’ I had no reaction. She kept saying ‘Take it down. It’s pornography!’ ” he said.

“The ones who complain are the old people,” he said.

The photos will be on display until May 18.

Additional reporting by Jennifer Bain