The 34-year-old actress, who starred in "Turn: Washington's Spies", a war-era drama, detailed her accusations in a lengthy Instagram post yesterday.
Lind said she was "disturbed" after seeing a photo of ex-US President Barack Obama with the 93-year-old Bush, the 41st American president, the Daily News reported.
"I found it disturbing because I recognise the respect ex-presidents are given for having served. And I feel pride and reverence toward many of the men in the photo. But when I got the chance to meet George H W Bush four years ago to promote a historical television show I was working on, he sexually assaulted me while I was posing for a similar photo," Lind wrote.
Lind had met Bush during a special screening of the show in 2014, a week before its premiere.
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"We were instructed to call him Mr President. It seems to me a President's power is in his or her capacity to enact positive change, actually help people, and serve as a symbol of our democracy. He relinquished that power when he used it against me and, judging from the comments of those around him, countless other women before me," Lind wrote.
In the past several weeks, dozens of women have accused media mogul Harvey Weinstein of sexual assault and harassment, and made similar claims against other actors, producers, directors, photographers and musicians.
Bush did not deny the allegations in a statement.
"President Bush would never - under any circumstance - intentionally cause anyone distress, and he most sincerely apologises if his attempt at humour offended Ms Lind," his spokesman told the Daily News.
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