As embattled New York City Mayor Bill de Blasio was heckled while addressing new NYPD officers at their graduation Monday, a police department across the country was investigating who was behind the ambush of two LAPD cops targeted Sunday night. Meanwhile, the Flagstaff Police Department in Arizona was mourning Officer Tyler Stewart, shot and killed Saturday while responding to a domestic violence call. Throughout the United States, police departments have issued warnings and updated policies in response to the fatal shootings of two NYPD officers two weeks ago and other recent attacks on officers as tensions between departments and the public they serve reached a boiling point. 

Such precautions, including ensuring officers have a partner when they are out on patrol and reminding them to be vigilant, have been taken in New Jersey, Pennsylvania, West Virginia and beyond. But such warnings run the danger of creating an overreaction that might do more harm than good, according to Jack R. Greene, a criminology and criminal justice professor at Northeastern University in Boston. Increased vigilance may cause an officer to deem someone a threat who is actually harmless, he said.

“In one instance, you can understand the sensitivity of police nationally to have two officers in New York fundamentally assassinated. The police nationally are sensitive to violence that they might encounter,” said Greene, who has served as a consultant to the LAPD and the Philadelphia Police Department. “The concern is not to overreact. Even though this is a horrific event, this is a rare event. If you develop a policy on rare events, you make things more difficult.”

In 2013, 27 officers were “feloniously killed,” a 45 percent decrease from the 49 officers who were killed in 2012, FBI statistics show. While there are no official statistics for 2014, the Officer Down Memorial Page, a website that pays tribute to officers killed in the line of duty, reported 47 law enforcement officers killed so far this year -- a 75 percent jump from 2013.

Conversely, there were about 461 “justifiable homicides” by law enforcement in 2013, or cases where a felon was killed by an officer in the line of duty, FBI data show. But that stat has been widely reported as flawed since numbers are self-reported by departments and exclude several states.     

Maria Haberfeld, a former lieutenant in the Israeli National Police and a professor at John Jay College of Criminal Justice in New York, said it’s possible, but unlikely the precautions will result in more police-involved shootings like the ones in Ferguson, Missouri, and Cleveland where two black youths were killed in recent months by police. What is more possible is that police officers across the country will be more "stressed," she said.

“Definitely police officers are on alert right now. Police subculture is always filled with what we refer to as ‘war stories’ that are based on experiences of other police officers who were hurt in the line of duty and right now these stories are amplified by what is happening around the country,” Haberfeld said in an email. “Will it make officers more inclined to use deadly force? Possibly, but I think that it will be rare. Instead they will be much more alert and stressed, but not necessarily trigger happy.”

The Newark Police Department in New Jersey is warning officers not to go on patrol alone, the Associated Press reported, while Pittsburgh police are assigning partners to officers who don’t normally have one in light of a vague threat of attacks on cops and white people in the area, the Pittsburgh Post-Gazette reported.

In Seattle, police haven’t issued specific warnings, but the killings of NYPD officers Wenjian Liu and Rafael Ramos two weeks ago serve as a reminder of the dangers cops face, said Detective Drew Fowler, a spokesman for the department. “The reality is that police work can at times be a dangerous profession and our officers are professionals and we’re aware of that fact,” Fowler said. “It means doing what’s right and remaining vigilant.”

There was a similar sentiment in San Diego, about 120 miles south of where shots were fired at two LAPD officers Sunday night while they were responding to a call. "The San Diego Police Department works closely with our law enforcement partners and our community members to identify all types of potential threats.  We will continue to be vigilant as we go about our duties to safeguard our fellow citizens and our city. As always, we remind the community that if you see something, say something,” the department said in a statement sent to International Business Times.

An LAPD lieutenant told the Los Angeles Times everyone is “keenly aware of what happened in New York.”  An LAPD spokesman told IBTimes Monday there is a person of interest in the local case, but no suspects had been identified.

The deaths of Liu and Ramos in New York further fueled tensions after their killer, Ismaaiyl Brinsley, suggested he ambushed the officers in retaliation for the deaths of Michael Brown in Ferguson, Missouri, and Eric Garner in Staten Island, New York. Anti-police sentiment characterized protests in support of Brown and Garner, and anger grew after grand juries chose not to indict the white police officers involved in their deaths.

De Blasio drew the ire of the police department after saying earlier this month he has told his half-black son, Dante, to be wary of interactions with the police. The city’s police unions said the mayor had blood on his hands in the deaths of Liu and Ramos, and the officers those unions represent displayed their anger at de Blasio by turning their backs on him when he addressed the officers’ deaths at a hospital last week.

He was also the target of a heckler at a NYPD graduation ceremony Monday. “You will confront all the problems that plague our society -- problems that you didn’t create,” the mayor said. The heckler shouted back, “you created them.”

While tensions ran high in New York, a police officer was killed in Arizona. Stewart, 24, died after being shot multiple times after asking if he could pat down a man for weapons while responding to a domestic violence call, the Associated Press reported.

The killings in New York and Arizona should not be treated as a trend, Greene said. Brinsley was reported to have been mentally ill, and domestic violence suspects have a “propensity for violence,” Greene said. Most police officer deaths occur in traffic incidents, not violent situations, he added.

“The problem is you can’t lump these into the same category,” he said. “The NYPD situation was an assassination. The Arizona police officer goes to a domestic disturbance case and it goes south. You can’t treat every police death as an assassination.”