Robert F. Kennedy Jr. responded to an accusation that he sexually assaulted a family babysitter at his home by brushing off the incident, asserting that he is not a “church boy” and had a “very rambunctious youth.”

In a wide-ranging report by Vanity Fair, the former employee accused the independent presidential candidate of groping her in 1998.

Eliza Cooney, who was hired in the fall that year as their part-time babysitter, was 23 years old at the time of the alleged incident. She moved into the Kennedy’s home in Mount Kisco,...