Statistics from this CDC document.

Overall death rates for all women, young and old, black and white, dropped during the war. In 1940, the death rate for white women of all ages was 8.8 per 1000 and dropped steadily to 7.5 per 1000 by 1945. For black/Hispanic/Asian/Native American women (classified as "nonwhite" in this document), the rate dropped from 15 per 1,000 to 11.9 per 1,000.

Suicide was a major cause of death for Americans (you can find the chart on page 99 and the source data on page 373). During the 1930s, about 15 per 100,000 people killed themselves every year. This dropped precipitously during the war, from 14.3 per 100k in 1940 to 12.7 in 1941, 11.8 in 1942, 10.0 in 1943, and 9.6 in 1944, returning to 10.7 per 100,000 in 1945. The suicide rate climbed again to 11.1 per 100,000 in 1946 but stayed below that rate through 1960, a level not seen since the turn of the century.

Here's a screenshot of the table which breaks this down by gender and race.

For white women and men, the suicide rate dropped steadily throughout the war, rebounding a bit in 1945 when the war ended. For nonwhite women and men, the suicide rate began increasing again in 1944. It's very sad to note that while suicide rates for nonwhite Americans were lower before the war, those rates climbed again and actually passed prewar levels in the late 1950s, when white Americans continued to have a suicide rate 1/3 lower than prewar levels.