In terms of form, these two works of literature are quite different (The Crucible is a play by Arthur Miller written in the 1950s, and The Handmaid's Tale is a contemporary novel by Margaret Atwood). But there are a number of thematic similarities. Both works could be said to contain feminist themes: the Salem Witch Trials as portrayed in The Crucible were very much a product of a society where women were second class citizens (one theory regarding the reason the young girls made so many accusations against their neighbors is that they enjoyed being the center of attention, something not afforded them as servants and as females in a Puritan society).
Along these lines, the theme of youthful female sexuality as a threatening force is also fairly central. In The Handmaid's Tale, women's sexual pleasure is forbidden and young, fertile women are imprisoned and forced to bear children for women who cannot get pregnant. In The Crucible, the young servant girl Abigail uses her sexual wiles to try and seduce and manipulate John Proctor away from his wife Elizabeth. In both cases, women are enslaved and prevented from realizing their full potential; in Atwood's work, women are prevented from functioning as anything other than chattel and baby machines, while in The Crucible the servant girls vie with one another for the few eligible men in the village so that they can escape the drudgery of working as servants.
Female sexuality is also regarded as a rather mysterious force in both stories. In Atwood's novel, men forbidden to have sex with anyone but their wives and the surrogate mothers of their children seek illicit sexual pleasure by treating the surrogates, including Offred, as prostitutes, giving them revealing clothing, cosmetics and other gifts. In The Crucible, the girls gather in the woods at night to use rituals and folk magic learned from Tituba to learn the names of their lovers and future husbands. It is within this mysterious setting that whispers of witchcraft in the village are first catalyzed, and these activities borne of normal adolescent sexual curiosity are tinged with the supernatural, and the repressive nature of Puritan society causes these feelings to erupt in what was later called by historians an episode of "mass hysteria." This psychological term (from the Latin and Greek words word for "womb") may also be ironically applied to The Handmaid's Tale, since it is fear of the power of female sexuality that eventually leads to the enslavement of women and the limiting of their sexual expression to the function of childbearing.