As Rose Houston returned from a short shopping trip along upper Georgia Avenue one morning last month, a man approached her a few doors from her home on Madison Street in Northwest. Identifying himself as a plainclothes police officer, the man accused Houston of using a counterfeit $20 bill to pay for one of her purchases.

Houston said she denied using counterfeit money, but that the man escorted her home and told her he would have to take all the money in the house.

Within three hours, the man persuaded Houston, 82, who said by then that she had become frightened and confused, to hand over to him -- a stranger -- all of the money she had stashed away in her house and most of the money in her savings account -- more than $1,000.

It was all a con.

Houston is one of more than a dozen District residents who have been conned out of a total of more than $10,000 in a growing number of scams that police call The Fake Police Officer Scheme.

In the past month, according to the Metropolitan Police Department, about 18 persons have reported handing over cash and jewelry to well-dressed men and women who claim to be plainclothes police officers or federal investigators. The average amount lost has been about $200, police say. But, last week, an elderly woman in Northeast lost $4,500 -- most of her life savings -- in the scam.

While these incidents are distinguished by their locations and victims -- senior citizens in the neighborhoods of Petworth, in Northwest, and Eckington, in Northeast, of the 4th and 5th police districts -- police say that residents of all ages throughout the city are regularly victimized by a variety of con artists' schemes.

According to police records, there have been more than 500 cases involving fraudulent schemes in the District in the first eight months of 1982, compared to more than 900 in all of 1981. At least 78 of the frauds that have occurred so far this year involved impersonators and persons who got away with more than $100, according to records.

Police Det. James Colbert of the check and fraud section said department statistics reflect only a portion of the scams that take place since scores of residents never report the scams to police.

"You're apt to get persons under 60 to report it more than those over 60," Colbert explained. " Elderly residents tend to think they'll appear foolish. They're embarrassed."

Police in the 4th and 5th districts say they are flooding neighborhoods with composite drawings of three male suspects and flyers detailing the scam.

Sgt. Dennis Hyatter told residents who met at the 4th District police station last week that though there are variations, the scam usually works this way:

Well-dressed young men or women claiming to be police officers persuade their intended victim to let them into his home where they either ask the person to turn over all of his money or search for it themselves, telling the person that serial numbers or fingerprints on the money are needed for a criminal investigation.

In a variation of the basic scam, the persons claiming to be police officers ask the intended victim to help catch a dishonest teller by withdrawing large amounts of money from a bank and giving it to them so the money can be checked for fingerprints, after which they say it will be returned.

Knowing how real police operate is the best way to avoid being taken by this type of scam, Hyatter told last week's meeting. "People are going to have to be cognizant of the responsibilities of the Metropolitan Police officer, what the law is and how we do our jobs," he told a group of about 40 senior citizens. He explained that real police officers:

Do not confiscate money or search a house without proper authority. Unless a police officer is in actual pursuit of a suspect, he must have a warrant to enter a home without permission. Hyatter told residents they should not hesitate to demand more identification of anyone who claims to be a plainsclothes officer or to deny anyone claiming to be a plainclothes officer entrance into their homes without a warrant.

Have an identification folder with a photo and either a gold or silver badge. Persons can get uniformed police officers to come to their homes to identify a plainclothes officer by dialing 911.

None of the victims has resisted the fake police officers yet, police said, and no one has been injured. Check and fruad division's Colbert said most persons who commit cons are not violent: "With them it's a mind game. They'll talk you out of your money."

"The elderly are a con man's dream," Colbert said, explaining that they are generally more respectful of authority and trusting of the police and therefore less likely to resist or question those who impersonate police officers.

Rose Houston's eyes began to mist when she recalled the events that followed her outing on the morning of Sept. 21, the day she was swindled out of her money. "I was walking on down the street not paying attention to nobody when this man walked up beside me," she recalled last week.

Though she said she was suspicious from the start, Houston nevertheless didn't resist. "Look like to me I was hypnotized, couldn't get myself together," she said, shaking her head at her own actions.

After Houston and the man got to the brick row house she shares with her 64-year-old daughter, the man searched the house and took more than $200 in a Christmas savings envelope that was hidden in a shoe box. Soon the man was joined by two women and another man. Houston said that next, the man she had met on the street drove her around the city, ending up at the woman's bank. There, she was instructed to withdraw $850, most of the money that she had in a savings account. The man took the money, Houston said. After again being driven around the city, Houston said she was finally released miles from her home.

Houston said she had been saving the money in her bank account, adding a little bit every month from her Social Security check, to help pay medical bills should her health fail.

Like many victims, Houston said she has been fearful and suspicious of others since the incident, but declares that she will not shut herself away because of it.

Her voice laced with fresh defiance, Houston mused, "People tell me now not to do this or go that place but I can't do that."