A three-judge panel of the U.S. Court of Appeals here ruled yesterday that the General Services Administration was wrong to fire an employe for stealing from the government through welfare fraud, and ordered the employe reinstated and awarded back pay.

Overturning a decision of the Merit Systems Protection Board, the judges said Ruth O. Gloster's 1980 guilty plea to welfare fraud had no bearing on her performance in her job as a GSA janitor and cannot be the basis for firing her.

An indictment returned against Gloster alleged that over a period of 6 1/2 years she collected $16,000 in welfare payments while employed by GSA. She pleaded guilty to one count of making a $314 false claim against the government, saying she had taken the money to ensure that she and her three children could survive on her salary of $11,500 a year.

GSA fired her in 1981.

Under the provisions of the Civil Service Reform Act of 1978, Gloster may be fired only if it would "promote the efficiency of the civil service," according to the unanimous decision by Appeals Court Judges Patricia M. Wald, Harry T. Edwards and Senior Circuit Judge Luther M. Swygert.

The court found that GSA had failed to establish a connection between Gloster's guilty plea and her job, where she was considered a "good employe," in the words of her supervisor.

Royce C. Lamberth, chief of the U.S. Attorney's civil division here, said yesterday, "I am surprised that a court would rule that someone who stole from the government cannot be fired."

Mary Jacksteit, deputy general counsel of the American Federation of Government Employees, which represented Gloster, said, "We think it's a very significant decision. We have been attempting to establish that under the Civil Service Reform Act, a person cannot be fired for off-duty misconduct, including a criminal offense, unless there is a connection with his or her job."

Gloster could not be reached for comment.

Government officials said yesterday there are no clear-cut rules concerning criminal conduct and government employment, either in hiring or firing decisions. While an offense committed on the job is considered cause for firing, government agencies and the Merit Systems Protection Board are required to take into consideration a number of factors in deciding whether a criminal conviction for off-duty conduct warrants rejection of a job applicant or termination.

"Determinations are made on a case-by-case basis," according to an Office of Personnel Management spokesman, who said there are no statistics on the number of such firings.

Twice before, appeals courts in other jurisdictions have ruled that government employes may not be fired because of criminal convictions. In the most recent one, the Ninth Circuit Court of Appeals in California ruled earlier this year that a Navy employe could not be fired after he was convicted of sexually molesting his daughter.

However, attorneys for both sides said yesterday's decision was the first time that a firing had been overturned when the offense involved stealing from the government.

In discussing the case, Jacksteit of the government employes' union drew a distinction between stealing directly from a government agency while working for that agency and stealing from the government as a whole while off the job.

"If you're stealing directly from your employer, obviously there's no problem with firing the person," she said. "She was not stealing on the job. She was not taking stuff out of desks."

Gloster began working for GSA's Washington region in 1966 and had been reprimanded only once, for failing one day to empty trash baskets on time. In 1972, she was laid off and began receiving welfare payments from the District and federal governments. After she resumed work that same year--working the early morning shift at 1405 I St. NW--she continued to collect the payments, the appeals court said.

When Gloster heard a news report on the radio that the government was cracking down on welfare fraud, she decided to terminate the payments, according to the government's brief in the case. She received a suspended sentence and three years' probation, agreeing to repay the government at the rate of $10 a month and to perform 100 hours of community service. She complied with all the conditions.

GSA said Gloster occupied a position of trust, since she was expected to maintain the confidentiality of government documents. Because she was a government employe and had violated that position of trust, GSA fired her, saying employes who abuse that bond of trust must be removed for the health of the agency.