Maybe, maybe not.
From Wikipedia: Since the 1940s, rumors have circulated that Hoover was gay. There are speculations that Clyde Tolson, an associate director of the FBI and Hoover's primary heir, may have been his lover. Hoover hunted down and threatened anyone who made insinuations about his sexuality. He also spread unsubstantiated rumors that Adlai Stevenson was gay to damage the liberal governor's 1952 presidential campaign. His extensive secret files contained surveillance material on Eleanor Roosevelt's alleged lesbian lovers, speculated to be acquired for the purpose of blackmail.
Some authors have dismissed the rumors about Hoover's sexuality and his relationship with Tolson in particular as unlikely, while others have described them as probable or even "confirmed", and still others have reported the rumors without stating an opinion. Hoover described Tolson as his alter ego: the men not only worked closely together during the day but also took meals, went to night clubs and vacationed together. This closeness between the two men is often cited as evidence that they were lovers, though some FBI employees who knew them, such as W. Mark Felt, say that the relationship was merely "brotherly." However, former FBI official Mike Mason suggested that some of Hoover's colleagues were denying he had a sexual relationship with Tolson in an effort to protect his image. Upon Hoover's death, Tolson inherited Hoover's estate and moved into his home, having accepted the American flag that draped Hoover's casket. Tolson is buried a few yards away from Hoover in the Congressional Cemetery. Among those skeptical of claims that Hoover was homosexual is Hoover's biographer Richard Hack. Hack notes that Hoover was romantically linked to actress Dorothy Lamour in the late 1930s and early 1940s, and that after Hoover's death Lamour did not deny rumors that she had had an affair with Hoover in the years between her two marriages. Hack additionally reports that during the 1940s and 1950s, Hoover so often attended social events with Lela Rogers, the divorced mother of dancer and actress Ginger Rogers, that many of their mutual friends assumed the pair would eventually marry.
In his 1993 biography Official and Confidential: The Secret Life of J. Edgar Hoover, journalist Anthony Summers quoted "society divorcee" Susan Rosenstiel as claiming to have seen Hoover engaging in cross-dressing in the 1950s. She stated that on two occasions she witnessed Hoover wearing a fluffy pink dress with flounces and lace, stockings, high heels and a black curly wig, at homosexual orgies. Summers also said that the Mafia had blackmail material on Hoover, which made Hoover reluctant to aggressively pursue organized crime. Although never corroborated, the allegation of cross-dressing has been widely repeated. In the words of author Thomas Doherty, "For American popular culture, the image of the zaftig FBI director as a Christine Jorgensen wanna-be was too delicious not to savor."
Skeptics of the cross-dressing story point to Susan Rosenstiel's poor credibility (she plead guilty for attempted perjury in a 1971 case and later served time in a New York City jail) and say recklessly indiscreet behavior by Hoover would have been totally out of character, whatever his sexuality. Most biographers consider the story of Mafia blackmail to be unlikely in light of the FBI's investigations of the Mafia. Truman Capote, who helped spread salacious rumors about Hoover, once remarked that he was more interested in making Hoover angry than determining whether the rumors were true. Attorney Roy Cohn, an associate of Hoover during the 1950s investigations of Communists and himself a closeted homosexual, opined that Hoover was too frightened of his own sexuality to have anything approaching a normal sexual or romantic relationship. In his 2004 study of the Lavender Scare, historian David K. Johnson attacked the notion of Hoover's homosexuality for relying on "the kind of tactics Hoover and the security program he oversaw perfected guilt by association, rumor, and unverified gossip." He views Rosenstiel as a liar who was paid for her story, whose "description of Hoover in drag engaging in sex with young blond boys in leather while desecrating the Bible is clearly a homophobic fantasy." He believes only those who have forgotten the virulence of the decades-long campaign against homosexuals in government can believe reports that Hoover would allow himself to be seen in compromising situations.
Some people affiliated with Hoover, however, defended the claims that he had homosexual tendencies. Singer Ethel Merman, who was a friend of Hoover since 1938, stated in a 1978 interview: "Some of my best friends are homosexual. Everybody knew about J. Edgar Hoover, but he was the best chief the FBI ever had." Another FBI agent who had gone on fishing trips with Hoover and Tolson revealed that the director liked to "sunbathe all day in the nude." Hoover often frequented New York City's Stork Club and one observer soap model Luisa Stuart, who was 18 or 19 at the time told Summers she saw Hoover holding hands with Tolson as they all rode in a limo uptown to the Cotton Club in 1936. Novelist William Styron told Summers that he once spotted Hoover and Tolson in a California beach house and the director was painting his friend's toenails. Harry Hay, founder of the Mattachine Society, one of the first gay rights organizations, confirmed that Hoover and Tolson sat in boxes owned by and used exclusively by gay men at their racing haunt Del Mar in California. One medical expert told Summers that Hoover was of "strongly predominant homosexual orientation", while another medical expert categorized him as a "bisexual with failed heterosexuality."