The caller to the Phoenix-area Taco Bell said he was a police officer and informed the manager there was a thief on the premises. Someone’s pocketbook was missing, the caller said, ordering that a female customer be detained and strip searched in a back office.

But there was no theft. Investigators think the caller was an impersonator, possibly from north Florida, who has pulled the same stunt dozens of times nationwide since 1999 with alarming success.

The caller, who sometimes poses as a company official, has persuaded managers at restaurants and other stores to detain and search employees for drugs or money. Targets have included Taco Bell, McDonald’s, Wendy’s, Burger King, Ruby Tuesday, Applebee’s, Perkins and others.

The caller’s motive is unknown. Because his targets are primarily restaurants, one theory is that he is a disgruntled former fast-food worker. Some investigators think he may be a sexual deviant who enjoys exercising power over people.

The searches have included male and female victims. Some businesses have been sued, and some managers have faced criminal charges.

“It’s a terrible scam, and we feel badly for everyone who was involved,” said Bob Bertini, a spokesman for Wendy’s International, referring to incidents in February at four Boston-area Wendy’s outlets. “The people who were caught up in this scam thought they were responding to direct orders from the police, and the caller in this situation can be very convincing and persuasive.”

Authorities think the hoaxer is a man who uses a phone card. Some calls have been traced to a public telephone in Panama City, Fla. Police there are investigating, but spokesman Sgt. Kevin Miller refused to discuss details.

The March 22 call to the Taco Bell in Fountain Hills, Ariz., is believed to be the first time a customer has been the victim.

Maricopa County, Ariz., Sheriff Joe Arpaio is investigating an incident where the manager of a fast-food restaurant was duped into strip searching a customer in his jurisdiction. Arpaio is shown Friday in front of a sign for his notorious tent

In that case, the Taco Bell manager pulled aside a 17-year-old girl who roughly matched a description provided by the caller, Maricopa County Sheriff Joseph Arpaio said. Told she would go to jail otherwise, the girl submitted to the search as the caller remained on the line to direct it.

The manager is on administrative leave while the sheriff’s office investigates, Taco Bell spokeswoman Laurie Schalow said.

In Massachusetts, the caller could be charged with rape for one of the Wendy’s incidents, said Sgt. Victor Flaherty of the West Bridgewater police, explaining that the rape statute allows charges to be filed against someone for just directing such an act.

Flaherty said the managers in the local cases would not face criminal charges because police “felt they were victims, too.”

But Arpaio said he thought managers were “ignorant” to fall for the scam and should face criminal charges if warranted. He said investigators were considering whether to charge the manager in the Taco Bell case.

“It’s mind-boggling,” he said. “How can a responsible person in this world ever do what has been occurring just because some guy calls them on telephone and tells them he’s a cop?”