According to Politico.com, in 2000 - as Giuliani was beginning the not-so-secret extramarital marital relationship with Judith Nathan, the woman who eventually became his third wife - he billed obscure city agencies thousands of dollars in expenses for his police security detail in the Hamptons off Long Island, where Nathan was living.
For example, in one instance, $34,000 worth of travel expenses were placed in the budget for the New York City Loft Board.
"These were records that the city comptroller tried to get in the past, but the mayor's office said they couldn't be released because of security," Politico.com's Mike Allen told CBS News correspondent Byron Pitts.
Giuliani's campaign had this response, calling the story a non-issue.
"This is common practice," the campaign said in a statement. "The NYPD is responsible for providing security for the mayor of New York around the clock."
"It's clearly the responsibility of the NYPD to provide the mayor's security around the clock and that's what they did," Giuliani spokesperson Maria Comella told CBS News.
But the question isn't about his security detail. It's about how the expenses were billed.
"It's coming out at the worst possible time for Rudy Giuliani, just as voters in Iowa and New Hampshire are beginning to make up their minds finally," said University of Virginia political science professor Larry Sabato. "It reinforces his biggest problem, which is not just his liberal positions on social issues, but also the fact that he's had a very messy private life."
Giuliani was asked about the story at Wednesday night's Republican debate.
"First of all it's not true," he said. "I had 24-hour security for the 8 years I was mayor. They followed me everyplace I went. It was because there were threats, threats I don't generally talk about. Some of them have become public recently, most of them haven't. And they took care of me and they put in their records and they handled them the way they handled them. I had nothing to do with the way they handled their records. And they were handled, as far as I know, perfectly appropriately."