Rep. Joe Barton says the Capitol Police have opened an investigation against the anonymous woman accusing him of an affair and of sending nude pictures of himself to her.

The Texas Republican accuses the woman of engaging in “revenge porn” against him — giving to others, after a relationship is over, intimate photos that two lovers might freely share with one another.

“Revenge porn” is illegal in the District of Columbia, in Texas and in more than 30 states.

It is not publicly known whether the woman, who was interviewed by The Washington Post, is behind the Twitter account that posted the nude picture of Mr. Barton on Tuesday. The Post did not name her to protect her privacy.

“This woman admitted that we had a consensual relationship,” Mr. Barton said in a statement to The Post on Wednesday evening about the liaisons, which began in 2011. “When I ended that relationship, she threatened to publicly share my private photographs and intimate correspondence in retaliation.”

Elsewhere in the Post’s article, the paper wrote that the woman had secretly taped a 2015 phone conversation with Mr. Barton and shared the conversation with its reporters.

On the tape, Mr. Barton notes to her that sharing nude photos of him, as she apparently already had done with other women, could become a police matter — a statement of fact that she took as a threat against her.

“As the transcript reflects, I offered to take the matter to the Capitol Hill Police to open an investigation. Today, the Capitol Police reached out to me and offered to launch an investigation and I have accepted. Because of the pending investigation, we will have no further comment.” Mr. Barton’s statement read.

The recording suggests “a potential crime against me,” he said.

The Capitol Hill police did not comment Thursday to multiple news outlets either on The Post report or on Mr. Barton’s claim of a “revenge-porn” investigation.

Earlier this week, Mr. Barton had acknowledged that between his separation from his second wife and their official divorce in 2015, he had several consensual relationships with “other mature adult women.”

“I am sorry I did not use better judgment during those days. I am sorry that I let my constituents down,” he said.

Mr. Barton, 68, announced this month that he would seek re-election to a 17th term in his conservative Dallas-Fort Worth area district.

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