FARMINGTON — Police Chief Jack Peck told selectmen Tuesday that even if his department budget was doubled and he had 10 more officers, it is unlikely the home invasion and murder of 81-year-old Grace Burton in the middle of the night one week ago could have been prevented.

Peck said the investigation has included constant K-9 searches of the area, all of the storm drain covers have been pulled in hopes of finding the weapon, and a helicopter with high-tech gear has scanned the crime scene.

Police have followed up on more than 200 leads and more than 70 DNA samples have been analyzed, looking for a match from the intruder’s blood left in the apartment.

Town Manager Richard Davis commended the 2-minute police response from the time the wounded Burton called police at 1:03 a.m. to the time officers arrived. She died of her injuries later that night at Central Maine Medical Center in Lewiston.

Board Chairman Stephan Bunker said the unsolved murder has unnerved this small community, but the incident should be kept in perspective.

“I refuse to have Farmington painted by this one event,” he said.

Peck said people should be vigilant and aware of their surroundings, lock their doors and windows, keep in touch with neighbors, and call police right away if they see something suspicious.

Selectman Ryan Morgan asked if the board could do anything to help.

“The support of the community is what we need right now,” Peck said.

He said 20 to 30 investigators, including detectives from the Maine State Police and the Franklin County Sheriff’s Department, are on the case and meet every day to discuss the latest evidence and developments. Also assisting have been departments from Wilton, Jay, Waterville, the Maine Drug Enforcement Agency and the Massachusetts State Police.

Moreover, he said, the past year has been one of the busiest the department has had. Since Burton was stabbed by an intruder in her home at Margaret Chase Smith Apartments on Fairbanks Road on June 21, a mile from the Franklin County Sheriff’s Department, a man survived shooting himself in the head, someone was wielding an AK-47, and on Tuesday, police responded to a report that a person at Hippach Field on Main Street had a gun.

“We’ve had a high-profile case every month for this past year,” he said. “But the homicide is the big one confronting us now.”

Cases have included commercial robberies and thefts, a felony assault. a felony theft at Walmart by a gang from Portland, a sexual assault and a residential robbery and assault of a homeowner on Red Schoolhouse Road. And earlier this month, a University of Maine at Farmington graduate was shot and his friend charged with manslaughter.

Bunker pointed out that the department’s track record shows nearly all of those cases have been solved.

Peck said crime is increasing everywhere.

“The social fabric has changed,” he said.

He said he knew Burton and had talked with her several times over the years. He described her as a fine person.

“My heartfelt condolences go out to the Burton family,” he said.