Prince George's County Executive Lawrence J. Hogan proposed a $547 million budget yesterday that relies on a massive infusion of state aid to avoid deep cuts in county services and to reduce the real estate tax rate by 30 cents -- described as the largest reduction in county history.

Hogan and other county officials once predicted dire financial consequences, including drastic cuts in government services, as the result of the tax-limiting TRIM county charter amendment adopted by county voters in 1978. t

That will not happen this year because of a $14 million increase in state funding for Prince George's.

Hogan's budget proposal to the County Council would cut the property tax rate from $3.04 per $100 of assessed valuation to $2.74. The owner of a $60,000 home that was not reassessed this year would pay $80 less in taxes than last year. For the owner of a similar home whose property was reassessed, the reduction would average only $24. A third of the properties in the county are reassessed each year.

Although Hogan's budget proposes no major cutbacks in county services or programs, he has eliminated funding for 934 positions throughout the government that are now vacant.

In the Police Department, for example, Hogan has reduced the number of police officer positions from 864 to 840. Hogan said yesterday the current strength of the department is 840.

Despite such reductions, the Police Department, like the Fire Department, will get more money from the county next year.

The most severe cuts as proposed for the school system, where Hogan calls for closing 14 schools and an environmental center and eliminating 40 administrative positions as well as the Junior ROTC program.

Hogan cut $4 million from the $290.3 million request of the Board of Education, which already had eliminated more than 500 teaching and administrative positions and cut the money available for new books and other supplies.

Unlike last year, Hogan recommended no increase in fees for county services other than a $2-a-ton additional charge for dumping refuse at the county landfill.

Hogan said the county is spared the impact of TRIM this year because of the additional state aid, a larger county budget surplus -- $14 million -- than expected and across-the-board cost cutting.

"Without state aid we would have been faced with a very, very serious problem," he said.

In Annapolis the county's state legislators, all Democrats, who lobbied for the increased state aid claimed a large part of the credit for the tax cut and the avoidance of deep budget cutbacks. They also criticized Hogan, a Republican.

"The only way TRIM is working is because of what we have been able to garner from the state," said Sen. Arthur Dorman, chairman of the county's Senate delegation.

The legislators noted that Hogan came to Annapolis recently to testify in favor of measures that would have placed a limit on state spending. "Its looked great politically to say he was in favor of a limit but it was irresponsible considering the shape the county is in," Dorman said.

Members of the all-Democratic County Council, some of whom were briefed on the budget by Hogan yesterday, also gave credit to the state legislators.

"Without state aid, Hogan's budget would not include any tax cut," said council member, William B. Amonett. "The 14.3 million from the state translates into about 30 cents of property tax. Thank God for the General Assembly."

Other council members said Hogan's budget shows that the county, under TRIM, is being forced to rely much more heavily on the state to avoid the predicted fiscal crisis.

"What has happened is we are transferring the cost of local government from local government itself, to state government," said council member Gerard T. McDonough. "The property tax has gone down but the state income tax [half of which goes back to the county government] has gone up. The true issue is the total tax burden and Hogan has not reduced that."

Council members also chided Hogan for failing to make good on a promise he made campaigning for the executive's job in 1978 to actually cut the budget.

During that campaign, Hogan vigorously criticized his Democratic opponent, Winfield M. Kelly Jr., who maintained that the budget could not be cut but promised to hold future increases to 4 percent.

Although both Hogan's budgets as executive have shown increases in government spending, Hogan said yesterday that because inflation is so high, the increases he has sought, including the 2.5 percent increase for 1981, are the equivalent of an actual budget cut.

Among the budget's major proposed expenditures are $313.7 million for county schools and libraries, $34.6 million for police and fire protection, $3.9 million for the Corrections Department, $12.5 million for the Health Department and other human services and $25 million for debt service on county bonds.

Among anticipated revenues are $148.4 million from the county property tax, $82.6 million from the state income tax, $152 million in state aid and $26.2 million in federal aid.