The birth rate in the year that ended in June 1984 dropped to 65.8 for every 1,000 women of child-bearing age, the lowest rate this decade, reflecting the fact that women are waiting longer to have babies and are having fewer, the Census Bureau reported yesterday.

The bureau also found that after giving birth, women are going back to work sooner than in the past, creating additional demands for child-care facilities.

And it found that Hispanic women generally have the highest birth rates, black women the next highest and white women the lowest. In terms of income and education, women at the low end have the highest birth rates.

While the overall birth rate for all women of child-bearing age (18 through 44) continued to drop, for one group, those aged 30 through 34, it rose between 1980 and 1984. The bureau said this did not suggest a "baby boom" in that group but rather reflected the fact that for a variety of reasons -- careers, more education -- many women are waiting longer to have babies.

Key findings in the survey:

*For all women 18 through 44, the birth rate for the year ending June 1984 was 65.8 per 1,000 women, compared to 71.1 in 1980 and 70.5 in 1982.

*Of the women 18 through 44 who had given birth in the year before the survey and who therefore had infants under 1 year old at the time of the survey, about 1.5 million, or 47 percent, were in the labor force, a far higher share than the 31 percent recorded in 1976 and the 38 percent recorded in 1980. This means that women were going back to work at unprecedented rates.

*These women contributed to new demands for child day-care facilities for working mothers. The bureau said the Census of Service Industries showed that the number of establishments providing child care services increased from 24,813 in 1977 to 30,762 in 1982.

*Although the birth rate for all women 18 through 44 was 65.8 per 1,000, it was far higher for Hispanic-origin women, 86.1, compared to 72.2 for black women and 64.6 for white.

*17 percent of the women 18 through 44 who gave birth in the year ended in June 1984 were single, divorced or widowed, compared to 14 percent in 1980. Among women 18 through 24, the out-of-wedlock rate was 28 percent.

*Generally speaking, women with extensive education were likely to have lower birth rates than those with little education. Thus, the birth rate for women 18 through 44 who had not completed high school was 82 per 1,000, but for women with four years of college it was 72.2, and with five years, 55.9.

*Birth rates were also higher for low-income women -- 89 per 1,000 for those with family income under $10,000 a year, dropping to 46 for those with family income $35,000 or over.