YAKIMA, Wash. — Yakima city and police officials say giving each patrol officer a personal police vehicle to take home is paying off, and not just financially.

In addition to boosting a police presence, officials say off-duty officers responding in the vehicles have assisted on several high-profile cases in the past month. Among the cases officials pointed to were the robbery at the Grizzly Espresso stand Feb. 10 and the Jan. 27 abduction of a teenage girl.

Capt. Jeff Schneider, who heads the patrol division, said when police learned the teen was being taken toward Cowiche, they were able to notify two off-duty officers who were able to catch up to the car. He said those officers were 10 miles closer to the car the teen was in than other units in the city.

The car was eventually stopped and the girl was rescued by police, who also apprehended one of the teens accused of abducting her.

In the case of the espresso stand robbery, off-duty police officers heard the call on their radios and were able to respond, as well as spot a car stolen from the stand’s barista.

“Officers were coming in to work, and they were able to quickly respond to the scene,” Capt. Rod Light, police spokesman, said about the coffee stand robbery.

In May, the city agreed to spend $4.7 million, to be paid over the next six years, on the vehicles. City Manager Tony O’Rourke said the financing for the cars runs about $800,000 a year, which he said is essentially the same cost as the regular replacement of pool vehicles — but with less wear-and-tear on the cars.

“Anytime a piece of equipment is shared by three or four people, it goes south really quick,” O’Rourke said.

He said the cars are being paid for, in part, by the patrolmen’s association’s decision to forego pay raises for two years in order to get the cars.

O’Rourke and Capt. Jeff Schneider, who heads the patrol division, said putting more cars on the road, even if the officer is off-duty, increases police presence on the streets and deters crime.

O’Rourke said Coral Springs, Fla., purchased patrol cars for its officers as well when he was city manager there, and he said it helped reduce crime.

“It seems like everywhere you drive, you see a police car,” O’Rourke said. “It’s a big pucker-up effect.”

But research on the subject is mixed. Kristie Blevins, an associate professor at Eastern Kentucky University’s School of Justice Studies, said in an earlier interview that a reduction in crime might be the result of more convictions leaving fewer criminals on the street, or criminals going to areas where there are fewer police.

At least three major law enforcement agencies in Washington — the Tacoma Police Department, the King County Sheriff’s Office and the Washington State Patrol — assign personal patrol cars to officers.