Weinstein "made it clear that if she did not succumb to his demands or if she exposed his unwanted conduct there would be retaliation, including humiliation, the loss of her job and any ability to work in the entertainment business," the lawsuit said.
It alleged that the production company "facilitated, hid and supported his unlawful conduct" and that members of the board "knew or should have known" about his conduct and "did not act to correct or curtail such activity."
A representative for Weinstein declined to comment Thursday. More than 100 women have accused him of sexual misconduct ranging from harassment to rape since exposes published in The New York Times and The New Yorker in October.
The scandal has finished his career. He was sacked by his eponymous film studio company on October 8 and is already facing several other lawsuits.
Weinstein denies any allegations of non-consensual sex and has said there were never "any acts of retaliation" against women for refusing his advances.
Under US law, battery can include physical injury, but also offensive or insulting contact that includes offensively touching someone against their will.