King: A Life by Jonathan Eig:
Robert Kennedy, unconvinced, struggled to understand why King didn’t take the communist threat more seriously. At the very least, King’s ties to Levison damaged King’s reputation in Washington, where such things mattered. On October 7, the FBI formally requested permission to install wiretap coverage on King’s home and office in Atlanta. Three days later, Robert Kennedy signed the authorization. He also approved an FBI request for a wiretap on Bayard Rustin.
Years later, Robert Kennedy’s associates would argue that the attorney general had permitted the wiretaps because Hoover had pressured him to do so. In a series of 1964 interviews that would remain sealed until after his death, Kennedy said he believed that Levison was a communist and that King had fallen under Levison’s influence. “Their goals were identical, really, I suppose,” Kennedy said of Levison and King. But in those same interviews, the attorney general offered additional context for his capitulation. Hoover, he said, claimed he had dirt on the Kennedys, too, including a report about a liaison with “a group of girls on the twelfth floor … of the LaSalle Hotel.” Robert Kennedy said the liaison never happened, but he offered it as evidence of Hoover’s methods.