Rudy Giuliani could have a William Bratton problem. So far, Mr. Giuliani’s campaign for the Republican presidential nomination has gone more smoothly than expected. There have been few negative stories about the former mayor of New York City.

The questions surrounding Mr. Guiliani’s campaign mainly involve his appeal to socially conservative voters, and here, Mr. Giuliani even is making inroads. When scrutiny has been made of his record as mayor of New York City, it has focused on his relationship with the former New York City police commissioner, Bernard Kerik, who withdrew from a nomination to be the secretary of the Department of Homeland Security due to a flurry of messy personal problems.

There is another former police commissioner — William Bratton — to whom the Giuliani campaign should pay more attention, though. Mr. Bratton, who served as New York City’s top law enforcement official between 1994 and 1996, has a history of stabbing bosses — current and former — in the back.

Many New Yorkers might remember the circumstances of Mr. Bratton’s departure from the NYPD. A trenchcoat-clad Mr. Bratton appeared brashly in front of a NYPD squad car on the cover of Time magazine on January 15, 1996. The headline emblazoned above his photo read, “Finally, We’re Winning The War On Crime. Here’s Why.” Time’s cover implied that Mr. Bratton was the crime-fighting hero. Mr. Giuliani’s role as crime-fighter was reduced to an afterthought, at best. In the wake of appearing on the magazine cover and the tension that it created, Mr. Bratton resigned in March of 1996. It was thought that Mr. Giuliani had wanted him to leave.

Recent interpretation of history, in some quarters, has credited Mr. Bratton for the downturn in New York City crime. A March 24, 2007 Associated Press story, for example, was pro-Bratton: “Bratton’s forced departure from New York in 1996 began a debate that goes on even now: Does the credit Giuliani claims for the crime reduction really belong to Bratton?” Crime reduction numbers, though, improved under subsequent appointments by Mayor Giuliani, including Police Commissioner Howard Safir.

The threat from Mr. Bratton lies on two fronts. First, should he decide to, he could publicly attempt to neutralize one of Mr. Giuliani’s strongest selling points — his role in the historic reduction in New York City crime. Second, he could potentially feed to national political reporters off-the-record disparaging quotes and assessments of Mr. Giuliani. While such conversations take place “without fingerprints,” Mr. Bratton is popular with reporters. And, while he is now on the West Coast, Mr. Bratton maintains relationships with a national network of journalists from the cities where he has worked — Boston, New York, Los Angeles.

In November of 1996, Mr. Bratton committed a sin in urban politics —he floated the possibility of his own run for mayor of New York City against his former boss. Even when he formally announced his decision actually not to run for mayor, he took a shot at Mr. Giuliani. Mr. Bratton contrasted his deference to the interest of his then-wife, Cheryl Fiandaca, a lawyer turned television legal analyst, who eventually became a WABC reporter, to Mr. Giuliani’s handling of the career of his wife, Donna Hanover, a former WPIX news anchor. “I’d hate by my running to place her in a position where, like the mayor’s wife, she might have to give that up.” Mr. Bratton and his wife divorced soon thereafter.

When he served as Boston’s police commissioner between 1991 and 1993, Mr. Bratton behaved in a similarly less-than-loyal fashion. Five days prior to the 1993 mayoral election in Boston, Mr. Bratton went on record to criticize the then mayor of Boston, Thomas Menino, for purportedly failing to provide adequate funding for the police department. “The irony of this is, we have the cure for what ails Boston, we’ve found the vaccine — it’s the community beat officers … But nobody wants to pay for them,” Mr. Bratton said. “I’ve got the cure, and somebody has to pay for the vaccine, because I damn sure don’t have the money.”

Despite his pointed use of the word “nobody,” it was obvious that “nobody” referred to Mr. Menino That attack provided the perfect opportunity for Mr. Menino’s mayoral opponent to further criticize Mr. Menino for his “failed leadership.” This is unheard of in politics. It is comparable to the secretary of defense criticizing the president days before a presidential election.

Soon after the election took place, Mr. Bratton, in search of a bigger stage, departed from his hometown of Boston and joined Mr. Giuliani’s administration. Boston’s crime numbers plunged even further, like they would in New York, after Mr. Bratton’s departure.

Mr. Bratton is now the police chief of Los Angeles, but met with Mr. Giuliani earlier this month in an apparent effort to mend fences — the first such meeting in more than a decade. Yet, the former police commissioner merits further watching. Mr. Bratton’s pattern is to save his public fire for the day just prior to Election Day. The Giuliani campaign will have to keep one eye on its opponents — and another on Los Angeles.

Mr. Gitell (gitell.com) is a contributing editor of The New York Sun and was Mayor Menino’s press secretary between 2003 and 2006.