Mayor Marion Barry's decision to lay off 76 corrections employes during the District's 1980 budget crisis threatened security at the city's detention facilities and led to unguarded posts and severe staff morale problems, according to a General Accounting Office report released yesterday.

However, despite the disruption caused by the layoffs and other budget cuts, the city's Department of Corrections "adequately coped" with the problems, said the GAO, a congressional oversight agency that also examines the District's government operations.

The report added that the disruptions in services and security caused by the layoffs ended when the 1981 budget restored funds for the department. However, the GAO criticized the city for failing to fill corrections positions as quickly as possible. Corrections officials blamed the delay on slow procedures in the city's personnel office--a claim denied by personnel officials.

Regardless of who was responsible, "it is indisputable that the Department of Corrections continued to suffer a decline in correctional officer staffing for nearly a year after the hiring freeze was over, and the reasons for this decline were administrative rather than budgetary." Unnecessary delays are no longer a problem, the report says.

Barry declined to comment on the report yesterday, saying that he had not been briefed on its contents.

"Certainly, the department never lost control of any of its institutions," the report said. The city's detention facilities include Lorton Reformatory in suburban Virginia, and the D.C. Jail in Southeast Washington.

An anticipated $6.6 million shortfall in the corrections budget in 1980 prompted Barry to devise a savings plan that originally included laying off 225 employes, including 150 prison guards. But the number was later reduced and in July 1980 he dismissed 76 people--31 guards and 45 others.

Two months later, guards, who said they were concerned about inadequate staffing, particularly at the jail, staged a two-day wildcat guard strike. The guards returned to work after they reached an agreement with Barry in which the city agreed to negotiate with them about their grievances.

The GAO report says the corrections department fueled the decline in staff morale caused by the layoffs and created confusion by not communicating with mid-level managers and rank and file employes. "The biggest complaint from the employes of the department of correction . . . was the total lack of clear, reliable information available to them," the report said.

The communications breakdown caused employes to lose confidence in the ability of the department's top management, the report says. In addition, uncertainty about job security contributed to the higher-than-normal number of employes who left the department for other jobs in 1980, the GAO says.

The top management of the department has recently changed with Barry's appointment of a new corrections director, James Palmer, a former chief deputy U.S. marshal here.