The Nanny (1965)

Bette Davis is an English nanny whose charge is a rude 10-year-old Joey, just discharged from a disturbed children's home where he'd spent two years undergoing treatment for drowning his little sister in the bath. He returns to an unloving father, fragile mother, and doting nanny -- whom he hates. Suspicion arises again when his mother is poisoned, and Joey continues to insist Nanny is responsible. Joey contends the nanny was responsible for his little sister's death, and only the upstairs neighbour girl believes him.