So how does a local TV station cover a breaking news story about an $80 million Paul Gauguin masterpiece that was attacked at the National Gallery by a woman declaring that the painting’s semi-nudity is evil?

Well, if you’re Fox-owned-and-operated station WTTG, you blur out the nipples on the two semi-clad Tahitian women portrayed in the famous late-19th-century oil painting.

Only then, it kinda appears that Gauguin painted the women to be anatomically incorrect.

(The station did show viewers that Gauguin, in fact, had a better command of female anatomy, in its late local news, The Post’s Emily Yahr reports.)

And if you’re Allbritton-owned ABC affiliate WJLA, you go with the Bouncing Banner.

That is, you push up that banner of type that usually runs at the bottom of the screen, so it serves a dual purpose: conveying the salient point “Gauguin Painting Attacked,” while also modestly covering the native women’s breasts.

If you’re the Gannett-owned CBS station WUSA, you don’t show the painting at all in your promos, but you do let your viewers see the actual painting in your news coverage, by way of more clearly explaining the story to the audience.

And if you’re the NBC-owned WRC, you show a cropped version of the painting in your promos, so viewers only see the women from the shoulders up; but you let your viewers see the work of art, as Gauguin intended it, during your newscast.

What we appear to have here is yet another illustration of that old gag about how one man’s masterpiece is another man’s dubious taste.

“Two Tahitian Women,” valued at $80 million, sustained no damage in the attack. It’s the property of the Metropolitan Museum of Art in Manhattan, and it’s on loan as part of the National Gallery’s exhibit “Gauguin: Maker of Myth,” which opened in late February.

The painting, completed in 1899, depicts two women; one is bare-breasted, the other has a cloth draped over one breast.

TV stations are understandably very wary of women’s breasts ever since Janet Jackson showed us hers, by way of breaking up the monotony of CBS’s broadcast of Super Bowl XXXVIII in 2004.

Remember, it was the CBS stations that the Federal Communications Commission slapped with those hefty fines when the aging pop star experienced her wardrobe malfunction.

And it was NBC stations that stood to get socked in the wallet when organizers of the 2004 Athens Summer Olympics decided to expose the opening-ceremonies audience to classical Greek statues, and mythological gods and goddesses, in various states of undress so fashionable in days gone by. That inspired some to write nasty notes to the FCC, demanding to know whether it was going to let NBC subject the flower of American youth, watching at home, to such a wanton display of Greekness.

Non-fans of women’s breasts were very well represented among those who communicated with the FCC about that Olympics’ opening ceremonies, causing the FCC to ask NBC to turn over the tapes, sending chills down the spines of NBC station suits nationwide.

“My children saw an exposed breast during the opening ceremonies,” one complainant said, as if he or she meant it to sting.

“First we had to be subjected to the breast of Janet Jackson in the [Super Bowl and] now an even more gratuitous display of pornography an [sic] indecency during what was suppose [sic] to be another family viewing event,” chimed in another in writing.

On the Gauguin painting, “We are comfortable that showing the portrait as the artist intended was central to the telling of this story,” WUSA general manager Allan Horlick and news director Fred D’Ambrosi said in a statement, in response to our query.

WUSA, however, did not show the painting in its promos for the news story. But promos, of course, fall under “marketing,” not “news reporting.”

On the flip side, WJLA general manager Bill Lord told The TV Column of the Bouncing Banner: “I probably spent under 10 seconds making this decision.”

“I didn’t agonize about it. It seemed like the most tasteful thing to do on television,” he said. “I didn’t spend a great deal of time thinking about what the FCC would do or anything like that. “

He noted that the station did show the painting in full on its Web site.

“It really seemed like, given the audience of the two media, which was seemingly the correct answer for television.”

A museum visitor, identified in documents filed with the D.C. Superior Court as Susan Burns, 53, of Alexandria, allegedly grabbed the Gauguin painting by its frame Friday afternoon and tried to pull it off the wall. She then tried to bash the painting with her fist, but it was protected by a plexiglass shield, court papers said.

Word of the attack hit the press Sunday afternoon, and the local TV stations talked about it Monday in their newscasts.

Burns has been charged with second-degree attempted theft.

According to court papers, Burns told an investigator: “I feel that Gauguin is evil. He has nudity and is bad for the children. He has two women in the painting and it’s very homosexual. I was trying to remove it. I think it should be burned.” She also said she was from the CIA and has a radio in her head, according to Post reporting.

Burns had been scheduled for a “mental observation hearing” Tuesday, according to court papers. That hearing was postponed and has been rescheduled for Wednesday afternoon.