States were able to administer federal block grant programs reasonably well in the first six months after they took them over, the General Accounting Office concluded in a 13-state study released yesterday.

The congressional auditors found that states had made only minimal changes in the programs and had been able to cope with reduced funding. But it said more changes -- and more budget problems -- could be expected in the future.

Last year's budget reconciliation act gave the states the responsibility for administering nine block grants. Six of them -- for social services; low-income home energy assistance; maternal and child health services; preventive health and health services; alcohol, drug abuse and mental health services; and community services -- went into effect last Oct. 1. Three others -- covering programs in education, primary health care and small cities -- took effect after the GAO completed its survey in March.

The change from categorical grants (in which states and localities get federal money for specific purposes) to the block grants (in which the states have far more discretion in distributing the money) was also accompanied by budget cuts of up to 25 percent. But the GAO found that funds left over from the categorical programs and requirements for continued funding of some activities tended to minimize the budgetary impact on the states so far.

Because of some statutory restrictions and the short time available before the grants took effect, the states generally followed previous priorities under the health and community services block grants.

However, the situation was different with grants for social services and low-income home energy assistance, which previously had been allocated according to a formula. The GAO found that the 13 states had drawn down 96 percent of the social services funds made available to them during the first half of fiscal 1982. To compensate, seven states transferred 10 percent of the energy aid to social services.

The Texas Department of Human Resources cut services to the handicapped more than emergency family services, taking the view that the handicapped program should be handled by another state agency. Kentucky, meanwhile, eliminated day care services for the elderly and reduced homemaker services to give a higher priority to other programs.

Because the states already had experience administering grants in most of the areas, the GAO found that they had to make few administrative changes. However, states had more trouble with the community services grant because that money previously had gone straight to local organizations.

The GAO also said that a universal concern of the states was the uncertainty of block grant funding levels and their individual allocations.

Several states said that, while certain federal efforts were helpful, the shift would have been easier with more timely and complete information.

Michigan and Washington said federal officials had limited their comments to restating what was already in the legislation and regulations and telling them it was their job to implement the legislation.

Several state officials said they had to develop their own basic information by asking previous grant recipients. Four states said they turned to groups such as the National Association of State Mental Health Program Directors.

A primary goal of the move to block grants was to reduce federal red tape and regulations for the states. While state officials said it was too early to assess the situation definitively, they cited some cases where they could see a difference.

Florida officials estimated they would be able to save $1.2 million a year because of fewer applications and streamlined monitoring requirements. Pennsylvania anticipated savings of $5.2 million and California $200,000.

Massachusetts said it took only three days to complete an application for energy assistance, compared to 22 days when that was a categorical grant.

The GAO also found that many states have continued to follow federal standards for administering grants even though they no longer had to. Many states said they didn't want to change accounting systems for the block grants when they still had to follow prescribed standards for other federal grants.

And although the states were not required to hold public hearings on the block grants distributed by the Health and Human Services Department, 11 of the 13 states did.

The states expressed a good deal of confusion about whether they were still subject to certain "cross-cutting" federal regulations, such as those on employment discrimination and environmental protection. The GAO recommended that the Office of Management and Budget try to clarify this area.

Most states were still developing plans for auditing their block grant programs, but many officials were concerned about who would pay for the audits and whether agencies would be reimbursed.

The GAO plans to continue monitoring the 13 states, which account for 45 percent of the nation's population.