WOULD putting more women on the beat help curb police brutality?That provocative thesis lies behind a push in the nation's second-largest city to dramatically increase the number of women in blue. A City Council committee will take up proposals in the next few weeks that call for bringing the number of female officers in the Los Angeles Police Department (LAPD) up to at least 43 percent - the percentage of women in the general workforce here. The department is 13 percent female now. Sponsors hope to achieve "gender balance" not long after the turn of the century. Experts estimate that women now make up 10 to 13 percent of the officers in most metropolitan areas. Even with growing pressure to put more women in uniform, no city is likely to come near gender balance anytime soon. While many doubt Los Angeles can - and some believe it shouldn't try - any jump in the number of women wearing badges here would have impact elsewhere. "There has been a glass ceiling for women for a long time," says Rana Sampson, a researcher with the Police Executive Research Forum, a nonprofit group. "If the Los Angeles Police Department hires that many women, departments across the country are going to look at it to see the effect." Nationwide, women have been making steady but slow progress in piercing the traditionally male-dominated institution. A 1987 study by the United States Department of Justice showed that the average makeup of the nation's 59 largest departments was 9.9 percent female. The highest was Detroit (18.9 percent), followed by Pittsburgh (15.4 percent), and Washington, D. C., (14 percent). Experts say few departments yet approach 20 percent. "The encouraging thing is that the growth has been steady," says Susan Martin, a sociologist who has written a book on women in policing. "But I don't think there will ever be parity." Changes in size requirements and physical training, as well as a hiring boom, contributed to a growth in female officers in the 1980s. But Dr. Martin says the working environment - sexual harassment, shifts that disrupt home life, dangers of the job - still discourage many. The move to increase the ranks of female officers here is an outgrowth of the effort to reform the LAPD in the wake of the Rodney King beating. City Councilman Zev Yaroslavsky is pushing a package that, in addition to increasing the number of women in the LAPD, would promote recruitment of female candidates for chief of police, seek gender balance on the Police Commission board, and require the Commission to take steps to eliminate sexual harassment and discrimination in the LAPD. He is backed by Councilman Mark Ridley-Thomas, Police Commissioner Ann Reiss Lane, and women's rights groups. The reforms are aimed at promoting equal opportunity and treatment; a major thrust is the belief that a more female-oriented force would help reduce police brutality. Supporters cite studies indicating that female officers are more likely to use verbal communication skills than excessive force in confronting suspects. They argue it would lead to greater responsiveness to female victims of crime and violence. In its report, the commission that probed police brutality in the wake of the King beating, found that no women were among the 120 officers with the most use-of-force reports. "Men tend to want to fight a suspect into jail," says Katherine Spillar of the Fund for the Feminist Majority. "Women like to talk them into jail." Researchers say there is some evidence to suggest that policewomen are gentler on the beat. "There are departments where the organization is so strong that it resists any influence by the incoming minority," says Jim Fyfe, a criminologist at American University. The LAPD endorses the idea of more women, though it questions whether the ambitious goals proposed can be reached. To see that they are, Mr. Yaroslavsky wants to increase the percent of new recruits that are female each year, starting at 30 percent. He would also put $50,000 more into recruitment. Even with these moves, however, achieving parity soon will be difficult. Initially, backers talked of doing it by the year 2000. But that would require hiring almost 100 percent women. "To get that many women, we'd have to go out and pull them in with a net," says a critical LAPD recruitment officer. One suburban paper here editorialized that, while increasing the number of women is a good idea, setting a numerical goal could compromise hiring standards and "sap the public's confidence in its police."