Ms Perkins is one of scores of accusers who have come forward after a New York Times investigation into Weinstein's conduct.
Actress Rose McGowan claimed that she reached a $100,000 (£84,000) settlement with Weinstein in 1997 after an alleged incident in a hotel room at the Sundance Film Festival.
The New York Times said a legal document confirming the settlement stipulated it was "not to be construed as an admission", but intended to "avoid litigation and buy peace".
Allegations against the 65-year-old are subject to criminal investigations in London, Los Angeles and New York.
He is also under civil rights investigation in New York state.