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Missouri Gov. Eric Greitens has admitted to an affair, and politicians have been known to survive those. But that might not be the best way to describe his relationship with the hairdresser whose ex-husband has released an audio recording of her talking about their first encounter, just six months before the former Navy SEAL announced he was running for the office he now holds. On the tape, she says he invited her to his family home, blindfolded her, duct-taped her hands to a piece of exercise equipment and took a naked photo of her that he threatened would “go everywhere” if she ever went public.

Greitens and his wife issued a joint statement that his infidelity is between them and God. Them, God and the injured parties, maybe. Including the voters who were told hundreds of times about his record as a stand-up family guy.

Only the governor’s real problem is that his unfaithfulness is not the point, as much as he would like it to be. Because while cheating on his wife is not against the law, extortion and coercion are, and other aspects of what’s been alleged might be, too.

Missouri has no law against revenge porn but does have a law against invasion of privacy that could apply. Our state’s version of an extortion statute outlaws “stealing by coercion.” If he did duct-tape her to a piece of exercise equipment, that could involve false imprisonment and/or battery.

The governor, through his lawyer, has denied that he took a photo, threatened blackmail or was ever violent in any way. But the bottom line is that we do not yet know exactly what happened. Which is why, unlike some state lawmakers, we’re not calling for his resignation or impeachment, at least until we know more.

The public absolutely does, however, need and deserve the criminal investigation that Circuit Attorney Kim Gardner has said she’s launching.

The governor seems to put the onus for any problems going forward on the fact that “there will be some people who cannot forgive.” His wife, Sheena, asks “the media and those who wish to peddle gossip to stay away from me and my children.” This isn’t mere “gossip,” though, but a potential crime and certain breach of public as well as private trust.

Greitens should welcome the police investigation. Because if he broke no law, he more than anyone needs the public to hear that from a more credible source than his own lips have proved to be. And though there’s a high bar for libeling or defaming a public figure, making false allegations is also against the law.

FROM AN EDITORIAL IN THE KANSAS CITY STAR