Anne Arundel police said yesterday they have abandoned their search for the parents or guardians of a 21-year-old retarded man looking for his home. They are not convinced he has one.

Police found the man, who calls himself Jimmy Conners, in July outside a Burger King restaurant in Glen Burnie. He told officers he was left there by his parents, who seemed to come from the Washington area. But although Conners appeared to recognize areas of Arlington, he was unable to direct police to his home.

At the time, Det. Gordon Deans of the Anne Arundel police, who handled the case, believed Conners' story. But now he says that if Conners was abandoned by his parents, it was at least five years ago. Police cannot discover who, if anyone, has been looking after him since then. And Deans said until Conners accurately recalls his past, police are unlikely to find out.

All that Anne Arundel police know for certain, Deans said, is that Conners was taken in by San Diego, Calif., sheriffs in 1977. An FBI fingerprint check turned up the records of that encounter.

Conners told San Diego officials "that he came from Texas and that his family was in Texas, and that his father had died and he left," Deans said. "He then said he lived in a commune for a while and came to California, where he was found."

Conners said then that his name was Ronald Lee Middleberg, Deans said. But authorities in Texas could not find anyone in that state who might be his guardian or parent. When Deans mentioned the name Middleberg to the man called Conners, there was no sign he recognized it.

Deans said California officials placed Conners under care in California until 1978, when he disappeared without a trace. "Between '78 and here we're lost," Deans said. "We have nothing on him. Nobody can trace how he got here. But I think at this point we're not going to find Jimmy's parents. They aren't findable.

"At this point, unless we get a big break in the case, our investigation is going to end," he added.

Conners is now living in a home for the retarded in Anne Arundel County, and will soon undergo intensive psychiatric testing, Deans said, because Conners' health records in California did not indicate the same degree of mental impairment that Anne Arundel officials diagnosed in him.

"Hopefully, medically, they can begin to draw out some of the information," Deans said.