The chairman of the Prince William Board of County Supervisors announced Tuesday that he perceives a spike in violent crime and that he believes Prince William needs 260 more police officers — which would increase the size of the force by more than 40 percent.

Corey Stewart’s announcement of a crime wave is based on few statistics but instead on a handful of visible incidents that have spooked residents in the past four weeks.

The county has had one homicide in the calendar year, a puzzling and disturbing shooting in a Woodbridge grocery store in February. Three men entered the store, opened fire, and left without stealing anything, all in under nine seconds. A 21-year-old mother, Glenda Coca-Romero, was killed, and her co-worker at the store was injured.

Police have asked for information on the as-yet-unsolved murder and have offered an $11,000 reward in conjunction with the FBI. According to an affidavit, police have identified a suspect thanks to tips from community members.

Stewart also mentioned a fight in February between about 20 members of rival gangs at Potomac Mills Mall, which led to the arrest of three teenage boys.

And the weekend before Stewart’s news conference about crime, county police responded to three sexual assaults in the Manassas area. In two of the cases, suspects, who were known to the victims, were arrested quickly. A suspect has not been identified in the third case, in which a 40-year-old woman awoke to find a stranger assaulting her in her bed.

In early March, Stewart (R-At Large) sent an e-mail to county residents with the subject “Spike in Crime.” But Jonathan Perok, a police spokesman, said he was unaware of “any particular spike in crime” in recent weeks.

From 2011 to 2012, the county’s violent crime rate increased by 9 percent, driven mostly by a large increase in rapes, which included many rapes committed in prior years but reported in 2012. The rates of murder, aggravated assault, and property crimes all decreased in 2012. The police department has not yet made statistics available for 2013.

At Tuesday’s Board of County Supervisors meeting, Stewart directed the county executive and police department to study the recent crimes to see if they revealed any trends. And he asked that the findings be available in time for the supervisors to consider them in their budgeting process, which will end in April.

Stewart said his top priority for the fiscal year 2015 budget will be increasing the size of the county’s public safety staff. To fund the new hires, he has supported a tax rate that would raise the average residential tax bill by about 5 percent.

“We have not hired the number of officers required to keep up with the population over the past seven years,” Stewart said Tuesday. Citizens in the fast-growing county, he said, “are very concerned about this perceived or real spike in crime.”

He said that he would like to see the department of 610 officers grow to 870, ideally. In the past three years, the department hired 10, 12, and 14 new officers, according to Stewart’s staff.

“If we only hire five new police officers this year, we will be shirking our responsibility for the most important responsibility we have as a board, public safety,” Stewart said.

He drew a connection to several other issues that have come up frequently as the county formulates its budget: class sizes and sports fields. “It’s all interrelated. If the schools are overcrowded, if the kids can’t get onto the fields, it goes without saying that they’re going to find something else to do. And it might not be a very good thing.”

Supervisor Peter Candland (R-Gainesville), who has been the most vocal proponent of a smaller budget on the board, said he supported a study of crime in the county but was not convinced there was any unusual problem. “The experts are saying it’s not a trend. We need to listen to them very carefully before we make a budget decision based on a knee-jerk reaction,” he said. “We don't want to worry anyone if there’s not a problem.”