For context, one should note that the word "neuroticism" is not used as a regular English word, but is one of the "Big Five" traits in psychology, which comes from factor analysis of personality surveys. Its "definition" would be something like "An underlying quality that correlates with answering 'Agree/Strongly Agree' on these questions and 'Disagree/Strongly Disagree' on those questions". Damore did not note this in his memo, which made the statement more offensive than it should have been.
With that established, if we go to Wikipedia...
https://en.wikipedia.org/wiki/Neuroticism#Age,_sex_and_geogr...
"A 2013 review found that groups associated with higher levels of neuroticism are young adults who are at high risk for mood disorders and women.[22]
For sex, the same review found that "research in large samples has shown that levels of N (neuroticism) are higher in women than men. This is a robust finding that is consistent across cultures. This is especially the case during the reproductive years, but is also visible in children and elderly." It furthermore said that EEG responses showed clear differences between the sexes in individuals with high N levels, but no functional MRI studies have yet been performed to investigate the differences in sex regarding N. However, there is a reason to suspect physiological differences to play a role because of previous studies that showed for example, a correlation between the size of the subgenual anterior cingulate cortex and N in female teenagers, so "the issue of sex differences in N and the implications for understanding N’s neurobiological basis deserve more detailed and systematic investigation."[22] A 2010 review found personality differences between genders to be between "small and moderate," the largest of those differences being in the traits of agreeableness and neuroticism.[37] Many personality traits were found to have had larger personality differences between men and women in developed countries compared to less developed countries, and differences in three traits—extraversion, neuroticism, and people-versus-thing orientation—showed differences that remained consistent across different levels of economic development, which is also consistent with the "possible influence of biologic factors."[37] Three cross-cultural studies have revealed higher levels of female neuroticism across almost all nations.[37]"
The abstracts of both of the cited studies are visible, though the full articles seem to be behind paywalls.