University of Washington computer scientists have created a tool which analyses film scripts to consider the relative power and agency of characters in films. Their results showed women in more passive roles. See the press release from the University.
Read their paper for more about how the connotation frames were created and for detailed analyses of gender bias in movie characters:
Maarten Sap, Marcella Cindy Prasetio, Ari Holtzman, Hannah Rashkin, & Yejin Choi (2017) Connotation Frames of Power and Agency in Modern Films.
The Center for the Study of Women in Television and Film publishes regular reports on the employment of women as directors and producers in the USA TV and film industry. It also has some materials about screen roles.