Rudy Giuliani’s front-running presidential campaign has lost a key staffer with connections to Karl Rove. Margaret Hoover joined Giuliani’s Solutions America PAC in September to help direct fund-raising operations, but her greater value was to shore up the former mayor’s credentials with conservatives and to signal Giuliani’s seriousness about a White House run. Hoover, a great-granddaughter of the 31st president, was an intergovernmental-affairs aide to Rove. She also brought important national campaign experience to Giuliani’s presidential quest, having worked for Bush-Cheney ’04. Hoover, 29, says she’s departing to pursue the ever-popular “other opportunities,” adding that she’s “still supporting Rudy for president.” Giuliani’s inner circle is notoriously rough on newcomers, and this is the second recent turbulent episode for a Bush transplant: In February, he demoted Anne Dickerson, a former top Bush fund-raiser, after lost Giuliani strategy documents turned up in the Daily News. “Margaret did a tremendous job helping the exploratory committee get started and we wish her the best of luck in future efforts,” says a Giuliani spokeswoman.