You may find some information on this in the Representative Bureaucracy literature. Ken Meier and a few other folks maintain a spreadsheet of the literature here: https://d2y1pz2y630308.cloudfront.net/6327/documents/2019/4/RBdatabase.html.
Off the top of my head, Jill Nicholson-Crotty and Meier measured the impacts female police officers have on sexual assault outcomes. Link here: Article Gender, Representative Bureaucracy, and Law Enforcement: The...
It's a controversial matter... Gender balance is very important at the workplace as it motivates both to work hard within friendly environments... In good governence practice we have participatory policy making and inclusiveness... If you exclude women then you will miss a big chance to utilize so many qualified people at the same time there will be lack of motivation and governing process does not represent the entire community... They will be lack of representation and public service dissatisfaction as their needs might not be fulfilled