Billy is a 43-year-old Providence, R.I., man who likes to walk into Dunkin Donuts shops, point his finger from inside the pocket of his tattered green coat, and demand "all of your money and a dozen doughnuts."

Billy has done this half a dozen times. But since is IQ is 61, the police usually catch him outside the shop munching on the doughnuts.

Then there is Charlie, a 26-year-old Baltimore man with an IQ of 46, who set a fire in a trash barrel in the hallway of his apartment building six months ago. The smoke panicked a tenant, who jumped out a window and died. Charlie was charged with murder.

Art, a 17-year-old with a 63 IQ, was cold on Jan. 8 when a chill hit Fort Worth. He walked into someone's house and took a coat from a closet. The next day, still wearing the coat, he strolled past the same house and was caught by the owner.

There are at least 25,000 retarded people in the nation's prisons, and some studies suggest that the number may be double that, or triple. This means that possibly one out of every 20 of the 500,000 prisoners in the United States is metally retarded. Their crimes include murder and armed robbery, but many are more innocuous offenses, such as "cheating" cab drivers because they didn't understand about paying.

As a rule, the retarded lawbreakers are in constant trouble. They commit the same crimes over and over again, are easilly caught by the police, and are repeatedly sentenced to prison.

Retarded lawbreakers can't think on their feet, so they get caught more often than other criminals, said Israel Perei, founder of a small program for retarded offenders at Camarillo State Hospital in Camarillo, Calif.

Ronald, for example, is a 33-year-old Rhode Island man who functions at the level of a 10-year-old. He is doing five years at the Adult Correctional Institute (ACI) for a bank robbery. Police had no trouble catching him because he signed his holdup note.

The retarded are convicted more easily and get longer prison sentences than the average lawbreakers because they seldom plea bargain and often confess, said Miles B. Santamour, of the President's Committee on Mental Retardation.

Donald, another example, is a 37-year-old Providence man with an IQ of 62. He has been arrested for breaking and entering at least 12 times, and each time he admitted the offense to the police.

Furthermore, the retarded usually serve all or most of their sentences, because they have difficulty meeting parole conditions, involving finding a job and a place to live, according to Louise Ravenel, head of the South Carolina Advocacy System and a former member of the President's Committee on Mental Retardation.

In some cases, said Robert Carl, Rhode Island associate director for retardation, retarded persons get arrested for acts other people can get away with.

There is Larry, a bizzare-looking retarded man in ill-fitting clothes who recently became entranced by a young woman at the Bonanza Bus station in Providence. Larry asked her for a date, the woman refused. Larry persisted, and finally he planted a kiss on her cheek, said Eilis Reaney, a state social worker who has worked with several retarded lawbreakers. Another man might have been considered amusing and rakish, but Larry was arrested by a policeman who had watched the scene, the social worker said. The charge was assault.

Another factor in the disproportionate number of retarded persons sent to prison, according to Santamour and several others, may be that many retarded offenders like prison and try to go back after they are released.

"It's a status thing," Santamour said. "Being a criminal gives one more status than just being retarded."

"I overheard one make a telephone call to his mother," said Brian Deery, medical director at the Rhode Island Department of Corrections. "He said he thought it was great here: he had chicken for dinner, he had his own room, he got to meet famous people, he felt he was somebody.

As a result, while the retarded represent about 3 percent of the population, they are about 9.5 percent of the nation's prison population, according to a 1971 study by the George Washington University Institute of Law, Psychiatry and Criminology.

About 27 percent of Georgia state prison inmates are retarded, according to a 1975 study by the Atlanta Association of Retarded Citizens. And at least 8 percent of the inmates of Tennessee's six reform schools are retarded, according to a study by officials there.

Findings differ because they are based on different kinds of tests and reflect varying opinions on the boundary between retardation and low-normal intelligence.

Santamour, using the American Association for Mental Deficiency's definition of retardation -- an IQ of 70 combined with an inability to meet standards of independence and social responsibility -- figures that about 5 percent of the nation's 500,000 inmates are retarded. And he believes the figure could be as high as 15 percent.

When defendants are identified as retarded, the courts often stop considering guilt or innocence, said Sister Arlene Violet, head of the Rhode Island Protective and Advocacy System, which has represented 40 retarded offenders in Rhode Island courts in the last year.

Instead, the issue becomes "Where can we send this person," she said. As a result, retarded persons are sometimes incarcerated for weeks or months in mental institutions, even though they may not have committed the offense that brought them to court, she said.

A retarded defendant also does not have any special rights before the court. In some states, such as Maryland, the question of competency to stand trial is based solely on the issue of sanity. "The retarded person is not mentally ill," said Nick Conti, medical administrator for the Baltimore County Supreme Bench. "He is legally responsible for his actions. There are no exceptions -- none."

In any case, there are so few programs for retarded lawbreakers that judges usually have little alternative but to imprison them.

Santamour said that there is virtually nothing for retarded offenders in Washington. He said he is extremely frustrated that, despite his position, he has been able to do little for two young retarded offenders he works with after hours.

In California, the only state-operated program for retarded offenders is serving 22 at Camarillo State Hospital, Camarillo, according to Perel, its founder. A handful of privately operated programs have begun recently, he said. Using the 5 percent figure, there are about 1,000 retarded offenders in California's state prisons, a figure that does not include juveniles or persons held in local or county jails.

In Texas, 70 juvenile retarded offenders are being treated in programs in Rusk and Houston, and another small program is scheduled to open soon in Longview. There are no programs for adults.

"No state is close to meeting the need," Santamour said.

"One reason is that many retardation and prison officials are just becoming aware of the scope of problem. But there may be other reasons for the slow development of programs for retarded offenders.

"These people are misfits," said Floyd Killough, program director at Rusk, Tex. "They don't fit into the corrections institutions and they don't fit into mental retardation services. The result is a pass-the-buck syndrome."

"There are other priorities," said John Moran, director of Rhode Island's Department of Corrections.

But some of the small programs that have been established are showing success.

The Mentally Retarded Juvenile Offender Program at Rusk has been operating for three years, making it one of only a handful running long enough to have statistical evidence of effectiveness.

The program provides treatment for 50 juveniles, who are committed by the court for crimes ranging from petty theft to armed robbery and even murder, Killough said.

Each youth has an individual treatment plan aimed at meeting his special problems. Each is provided with vocational training, which Killough noted is especially important for those who stole because they didn't know of any other way to get money. Those from rural areas might be taught farming, others might learn engine repair or woodworking.

Behavior modification, which encourages good behavior through a system of rewards and withdrawal of privileges, is used to eliminate improper behavior, such as a tendency to strike out at people, Killough said.

Many retarded offenders break the law because they don't understand the rules of society, can't control childish impulses, don't understand the consequences of their actions or don't know any way besides stealing to get food, Killough said in a comment that was repeated by several other program operators.

It is much easier to get at the root of such problems than to try to deal with more intelligent criminals such as "a guy who could be a mechanic but would rather rob banks," Killough said.

Of the first 22 teen-agers who went through the program, only three had been rearrested a year after discharge, Killough said. By comparison, the overall recidivism rate for juvenile offenders in Texas is 48 percent, and retarded offenders who are not helped are thought to do worse.

The successful graduates include a young man who is working on a loading dock and one who is working in a meat market. Another of the graduates, who was sent to the program after being arrested for theft and burglary, is going to school part time and is working as a janitor in a bank.

"We think our figures are good, but they could be better if we had better aftercare," Killough said. But when the youths are released from the program, they are on their own.

At the Lynchburg Training School in Virginia, 170 juvenile retarded offenders, many of whom are also emotionally disturbed, are spending six to 18 months in a program which, like Rusk, emphasizes behavior modification.

Scott Carroll, center director, said that 32 percent of the graduates of the 3-year-old program are subsequently rearrested and return to Lynchburg. Carroll said this is close to a total recidivism figure because "nearly all the graduates who bomb out are returned to the program."

The 32 percent figure compares with an overall recidivism rate of 70 percent for juvenile offenders in Virginia, he said. The success rate could be improved if retarded offenders could be eased back into the community through a system of half-way houses, he said, but no such system exists.

To those in the field the need to develop and expand programs like these is clear.

"If mentally retarded people are going to be accorded the privileges and the rights of citizenship, they also have to bear the responsibilities," Carl said. "If they hurt somebody or violate the law, they've got to pay some dues. I'm not asking for special consideration. I'm just suggesting that mentally retarded people need a program that ought to be part of our criminology system."

"What we are asking for," Santamour said, "is simple justice."