An 81-year-old Arlington woman who suffers memory lapses was placed in a taxicab by two county police officers who did not know her address and then taken to Alexandria, where she wandered for more than seven hours before a citizen came to her aid.

Arlington police are investigating the May 18 incident, according to Deputy Chief David Reiten, who said the officers' action was the product of "inexperience."

"There's a very thin line we must walk between responsibility to members of the community and infringement on their rights," Reiten said. In this case, "There's no question that they should have asked a few more questions. But that's hindsight."

"There's a gap in there -- we have no idea" what happened to the woman from the time she left the cab until a person found her walking near the George Washington Masonic National Memorial in Alexandria late that afternoon, Reiten said.

Arlington police began looking into their handling of the incident after receiving complaints from a resident, the deputy chief said. He said he expected to receive a full report today.

The two Arlington patrol officers, Erin Hine and Randy Bilder, met the woman when they were called to the Westover Supermarket by employes who suspected her of taking a package of hot dogs. When officers arrived, he said, supermarket officials said they did not want to press charges.

Hine and Bilder talked to the woman for several minutes, Reiten said.

"She was very straightforward . . . . She gives them a name, which turns out not to be hers. She gives them her date of birth, which turns out not to be hers." She had no identification with her, Reiten said. He said the officers called a telephone number on a card in the woman's purse, but no one answered.

At first, she was reluctant to tell the officers where she lived, he said. "From their perspective, she was being evasive."

After several minutes of questioning, he said, the woman told the officers she lived in Alexandria.

"What we had here was a five- to 10-minute encounter with a person who, by outward appearance, was in control of her faculties . . . . The officers decided she had the ability to take care of herself," Reiten said. The officers called a taxi and "thought she would give the cabby her address."

Shortly after the woman left Arlington in the taxi, a relative called county police and reported her missing, Reiten said. The cabdriver, meanwhile had taken the woman to Alexandria. The driver let the woman out near Rte. 1 south of Old Town, apparently when the fare exhausted the $13 she had with her, the deputy chief said.

Hine and Bilder will not be disciplined, but will be counseled to avoid similar incidents in the future, Reiten said.

"We will use it as a learning experience for these officers and others . . . to ask those few more questions, to take a little more time."

Hine has been with the police department since September 1984; Bilder was hired in August. Neither could be reached for comment yesterday.