The Prince George's County Council approved a $458 million budget yesterday that falls within voter-mandated tax limitations but will not reduce most homeowners' tax bills.

Under the new budget, which cuts back some services in most county departments, spending will increase by 3.5 percent over last year's level, compared to an areawide inflation rate of 8 percent in the past year.

Although Prince George's is the only local jurisdiction with a voter-approved limit on government spending, the county budget passed yesterday follows a trend of fiscal conservatism already established in other suburban jurisdictions in the Washington area.

Officials in the city of Alexandria and in Arlington, Fairfax and Montgomery counties have passed budgets that either keep taxes at their present level or increase them only marginally.

However, no jurisdiction, including Prince George's, has actually been able to reduce taxes, despite the calls for cutbacks that followed the passage of California's tax-slashing proposition 13 last summer.

Only one council member, Sue V. Mills, voted against the budget. Mills said she believed that cuts in the county schools budget were inadequate.

Under the budget for the year beginning July 1, a typical owner of a home that was assessed at $50,000 last year will pay $752 in county property taxes and $73.65 in park taxes, $11.50 more than last year.

However, the council's budget for the Washington Suburban Sanitary Commission should reduce the water and sewer payments of the average family by about $8 next year, to $176.50, according to budget officials.

This year, the council was forced to reduce the county's tax rate 27 cents-to $3.04-because of the TRIM charter amendment, which limits the total amount of taxes that can be collected by the county.

The rate cut mandated by TRIM is offset by the 9 percent inflation in the assessed values of homes, however, county officials said. The cost of county government thus will remain about the same for most homeowners for the second straight year.

Many of the council decisions on spending reductions followed closely the $458 million budget recommended two months ago by County Executive Lawrence J. Hogan.

However, the council revised Hogan's proposed spending priorities in several important areas:

The council added $2.9 million to the $275 million budget proposed by Hogan for the county school board. The increase still means, however, that the school board will have to cut $10 million from its own proposed budget.

The council cut $770,400 from Hogan's proposed budget for the police department, rejecting Hogan's request for 100 new sedans for administrative personnel and eliminating a new lieutenant colonel position that Hogan wanted to fill with a black from outside the department.

The council also set aside $1.8 million in a contingency fund for salary and cost-of-living increases for county employes. The funds would allow across-the-board cost-of-living increases of 5 percent for county employes, as opposed to the 3 percent proposed by Hogan.

Council members stressed, however, that because most county unions are still negotiating new contracts, the final decision on pay increases will depend on the outcome of Hogan's bargaining with the unions, who represent about 3,000 of the county's 6,300 employes.

Hogan aide John McHale distributed a statement yesterday afternoon that described Hogan as being "generally pleased" with the budget approved by the council. The statement said that Hogan, who campained vigorously for cuts in the school budget, thought that the council's school spending was "most generous."

It was on the school budget, which makes up almost 60 percent of the total county budget, that the council faced its most critical decisions.

Hogan proposed that$13 million be cut from the school board's proposed budget, including a reduction that would have lowered cost-of-living increases for the 13,000 school employes from 5 percent to 3 percent.

The council eventually added $1.8 million and transferred $1.1 million to Hogan's school budget, but council members emphasized yesterday that it was up to the school board to decide questions of salary increases and program cuts.

School board members have said repeatedly that they will honor the 5 percent increases they have already promised their employes, and that the council's reductions in their proposed budget may force them to fire dozens of employes and cut back or eliminate summer school, adult eduction, sports and other programs.

Nevertheless, council members said yesterday that they thought the cuts in the school budget should not affect programs. "We've provided them with enough to maintain a reasonable level of service," said council member Gerard T. McDonough. "Now it's up to the board to use their resources in the way they think is best."

The budget approved by the council yesterday will keep the county Department of Licenses and Permits at the same leveel of funding next year as this year. The budget for the Office of Central -Services-which coordinates informational and administrative functions for the county-will be cut from the $4.5 million spent this year to $3.9 million next year.

The budget also allows a $1 million increase-to $11.5 million-for the Fire Department, but only small increases for the Health Department and the Department of Public Works and Transportation.

Although most council members seemed satisfied that they had managed to balance their first TRIM-limited budget without damaging county services, several said before voting yesterday that they were worried about the county's future under the Proposition 13-style measure.

"This budget is a mild sample of what to expect next year," said council member Frank P. Casula. "And the following year will be a catastrophe for Prince George's County unless TRIM is modified or repealed."

"The county government will come under greater strain," said Council Chairman William B. Amonett. "This budget . . . represents the genesis of a new style of government in Prince George's-more creative, more innovative in its use of tax money."