The Prince George's County Council decided yesterday to cut 35.5 cents from the county tax rate, a reduction that will save the owner of a $65,000 home in Prince George's about $103 next year.

The council's tax rate cut, which will be formally approved today and go into effect on July 1, adds another 5.5 cents to the reduction recommended last month by County Executive Lawrence Hogan in his proposed $547 million 1981 budget.

The council, which has final authorizity over the county budget, currently is considering Hogan's recommendations and will approve a final 1981 budget on May 29.

Prince George's is one of the few jurisdictions in Maryland and the Washington area that has been able to give its residents a property tax cut, mostly because of massive doses of state aid.

The county tax rate also has been held down because of TRIM, an anti-tax charter amendment approved by county voters that limits tax collections to the 1978 level.

Both Hogan and the council were able to reduce taxes even further than the amount TRIM would require without seriously harming county services and programs because of a $14 million increase in funding from the state.

In order to give county residents a large tax cut, Hogan had proposed across-the-board reductions in most county agencies, including the elimination of more than 900 positions in county government that are now vacant, closing 14 public schools and reductions in the size of several park system programs.

Yesterday the council informally decided to restore many of the park system programs by increasing the park tax rate by 1.45 cents over the current 38.97 cents. The park tax, county property tax and an ad valorem sewer tax make up the total county tax rate.

The decision to restore many of the park programs -- including free use of summer playgrounds instead of the 25 cents a-day charge Hogan had proposed and maintenance of an eight-week long camp for underprivileged children that Hogan had cut to six weeks is part of the council's overall budget strategy of reallocating money from administration agencies and positions to social service ones.

As part of this strategy the council has decided to give $2.2 million more to the school board than had been allotted for school bus replacements.

Because of a change in state law, the buses do not have to be replaced this year and the council is recommending that the $2.2 million be used to reduce the number of school closings, and to continue an environmental camp and Junior ROTC program, both of which had been eliminated from Hogan's budget.

Council Chairman Parris Glendening said the council decided to reduce those agencies that don't directly serve the public by an average of 1.3 percent through cuts in upper management positions and duplicated services. Among the agencies expected to be affected by such cuts are the Department of Program Planning and Economic Development, Police and Fire Departments, and the Department of Public Works and Transportation.