Crooks said because her employer did business with Trump, she felt compelled to introduce herself to him. They shook hands and then, she says, he began kissing her, working his way from her cheeks to her mouth.
Crooks told the Times she felt violated by the incident. She also said she immediately told others about what happened, including her sister and her boyfriend.
During a highly charged interview with the Times Tuesday night, an agitated Trump denied the women's claims, saying "none of this ever took place."
In both the piece and on CBS "This Morning" on Thursday, reporter Megan Twohey said Trump began shouting at her as she continued to question him, accusing the newspaper of trying to sabotage his White House bid, and calling her "a disgusting human being."
Pressed about the alleged groping, Trump responded, "I don't do it. It was locker room talk," referring to the "Access Hollywood" tape.
He also threatened to sue The New York Times for libel.
In his letter to the Times, Kasowitz said "It is apparent from, among other things, the timing of the article, that it is nothing more than a politically-motivated effort to defeat Mr. Trump's candidacy.
"That is why you apparently performed an entirely inadequate investigation to test the veracity of these false and malicious allegations, including why there two individuals waited, in one case, 11 years, and, in another case, more than three decades, before deciding to come forward with these false and defamatory statements," Kasowitz continues.
"Clearly The New York Times is willing to provide a platform to anyone wishing to smear Mr. Trump's name and reputation prior to the election irrespective of whether the alleged statements have any basis in fact," the letter says.
Hillary Clinton's press secretary, Brian Fallon, dismissed the letter Thursday, saying: "Trump's lawyer's letter is meaningless. Baquet will line his birdcage with it."
And even before Kasowitz put pen to paper, three other women came forward to say Trump touched them inappropriately.
Mandy McGillivray told The Palm Beach Post Wednesday that the billionaire real estate developer grabbed her rear end 13 years ago, and on Wednesday night, a People Magazine reporter, Natasha Stoynoff, published an article on the magazine's website saying her forcibly kissed her prior to an interview at his Mar-a-Lago resort in Palm Beach, Florida in 2005.
Then there was Temple Taggart McDowell, who represented Utah in the 1997 Miss USA pageant , who told MSNBC Trump repeatedly kiss her on the lips without her permission, both during a pageant rehearsal and later, during a visit to Trump Tower in Manhattan at Trump's invitation.
A Trump spokesman said Stoynoff's account was a fabrication. The campaign has yet to specifically address McGillivray's claim.
As for McDowell, Trump told MSNBC "I don't even know who she is."
"She claims this took place in a public area. I never kissed her. I emphatically deny this ridiculous claim," he said.
The avalanche of bad news for Trump on Wednesday didn't stop there. As awareness of The New York Times story spread Wednesday night, a number of news outlets, including CBS News and BuzzFeed, reported that women who had participated in Trump's Teen USA beauty pageants said he frequently barged into their dressing areas as they were changing.
CBS News also broadcast a 1992 clip from an "Entertainment Tonight" Christmas special in which Trump us seen talking to a young girl on an escalator at Trump Tower, then turning to the camera and saying, "I am going to be dating her in 10 years. Can you believe it?"
On Thursday, as Trump awaited the Times' response, the candidate lashed out at his female accusers during an appearance in West Palm Beach, calling them "horrible people" and "horrible, horrible liars."
According to Trump, The New York Times story and subsequent reports by other news outlets are a "coordinated, vicious attack" by the media in cooperation with the campaign of Democratic presidential candidate Hillary Clinton.
"These vicious claims about me, of inappropriate conduct with women, are totally and absolutely false. And the Clintons know it," Trump declared.
The comments came shortly after he called a reporter "a sleazebag" for asking during a West Palm Beach business roundtable whether Trump had ever touched or groped a woman without her consent.
The business men and women seated at the table booed the reporter, who was quickly escorted out of the room. Trump never answered his question.
Meanwhile in Pennsylvania, Trump's running mate, Indiana Gov. Mike Pence, ditched the reporters who have been regularly covering his campaign.
Pence has not commented on the women's accusations against Trump.
His campaign told reporters Thursday morning that Pence was attending two fundraisers that were closed to the press. But his official Twitter account has shown him greeting voters at a restaurant and meeting with faith leaders.
One tweet on his account this morning said "We're glad to be back in Pennsylvania on the campaign trail!"
McCraw's response to Trump's demand for a retraction of the Times' article said "it would have been a disservice not just to our readers but to democracy itself" to silence the voices of the women quoted.
"The women quoted in our story spoke out on an issue of national importance - indeed, an issue that Mr. Trump himself discussed with the whole nation watching during Sunday night's presidential debate."
"Our reporters diligently worked to confirm the women's accounts," McCraw said. "They provided readers with Mr. Trump's response, including his forceful denial of the women's reports.
"We did what the law allows: We published newsworthy information about a subject of deep public concern. If Mr. Trump disagrees, if he believes that American citizens had no right to hear what these women had to say and that the law of this country forces us and those who would dare to criticize him to stand silent or be punished, we welcome the opportunity to have a court set him straight."
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