In family murders, men are twice as likely to kill family members as women (or at least twice as likely to be defendants, 65.5% vs 34.5%), but when women do kill family, they are much more sexist about who they kill.

"When a mother killed her own child, the offspring she killed was more likely to be a son than a daughter: 64% sons versus 36% daughters. But when a father killed his own child, the offspring he killed was about as likely to be a daughter as a son: 52% daughters versus 48% sons." And “When a son killed a parent, his victim was about as likely to be the mother as the father: 47% mothers versus 53% fathers. But when a daughter killed a parent, her victim was more likely to be the father than the mother: 81% fathers versus 19% mothers."

SOURCE: Murder in Families (ojp.gov)