Deluged with complaints from homeowners whose assessments have drastically increased, the D.C. City Council will shortly add a property tax relief clause to the fiscal year 1978 city budget.

About two weeks ago the Prince George's County Council, mindful of homeowners' anger over rising assessments, cut $5 million from the proposed fiscal year 1978 budget in order to reduce by 15 cents the property tax rate and another tax that affects nearly all homeowners.

A week ago the Montgomery County Council, completing work on its fiscal year 1978 budget, gave the school board only enough money to fund a 4.2 per cent employee salary increase instead of the 6 per cent increase agreed upon by the board and school employees.

The Council acted with the knowledge that the school board will almost certainly have to cut drastically school programs to make up the difference, but he Council majority felt that providing the money for the full salary increase would have made worse an already "intolerable (property tax) burden" on county homeowners.

As governments throughout the metropolitan area grapple with next year's budgets, their decision on what gets included and what gets excluded seem to be based on an almost obsessive concern with the impact upon the property tax.

There's a good reason for their sensitivity.

The continuing rise in the assessments on homes in recent years has sparked the establishment of both formally organized and informal home-owner groups that have pressured city, county and state officials to do something about the increasing taxes.

Elected officials, mindful of the political implications of the homeowners' dissatisfaction and of their jurdictions' strained fiscal resources, say they have been paring and trimming their budgets wherever possible in an effort to keep the property tax rate down.

Although the property tax rate will remain stable in nearly all of the nine metropolitan jurisdictions from which information was gathered, the actual property tax many homeowners will pay will increase due to rising assessments as the value of a home increases.

"Local officials in suburban areas can't control the assessment," said Alexandria City Mayor Frank Mann, "but we can control the tax rate. All of us in the whole metropolitan area have been made aware of citizens' feelings about the violent rise in (property) taxes."

Early this month Alexandria's City Council passed an $82.2 million budget which included a 5-cent decrease on the property tax rate. The cut, lowering the rate to $1.70 per $100 of assessed valuation, means that the owner of a $60,000 home, whose assessment has remained the same, can expect to pay $30 less in property tax.

The Council balanced its budget by deleting or deferring several street projects and by taking $3.5 million from a budget surplus. It also asked the school board to pare one item on its budget.

"I feel we can keep the tax rate stable and still maintain services, but we may very well have come to a point of not being able to fund certain programs, no matter how much we like them," Mann said.

"We've got to face up to the fact that the homeowners are at the end of their rope," he continued. "If we don't try to equalize the (tax) burden, we're going to kill the goose that laid the golden egg."

Mann was referring to the fact that for most jurisdiction in the metropolitan area, the property tax provides from 30 to 50 per cent of the revenue, and can be easily tapped for more funds. A penny increase on the tax rate can supply hundreds of thousands of dollars to the government's coffers.

Thus, the tax can be a quick source of money for officials seeking funds to pay the inflation-inspired increased costs of government.

Politicians throughout the area agree, however, that it's unfair - and politically unwise - to force one group of taxpayers to shoulder a disproportionate burden.

In Arlington 30,000 homeowners, 40,000 apartment dwellers, and commercial or industrial firms all pay property taxes. The homeowners pay more than half the property tax funds the county receives, according to County Board Chairman Joseph Wholey.

Wholey said the average homewoner in Arlington pays about $1,000 in property taxes. The average apartment dweller, through his rent, pays about $250. The disparity is roughly comparable in other jurisdictions.

Government officials in several jurisdictions have proposed increasing such sales and use taxes as those for cigarettes, alcohol, and food as a means of spreading the tax burder and taking some of it off homeowners alone.

The property tax burden results from combining the property tax rate with the soaring value of housing in the metropolitan Washington area. According to federal data cited in a Montgomery County government booklet, the average sales price of existing homes in the region has risen in recent years from $28,000 to $57,000 - an increase of 103 per cent.

Property assessments - since they're tied to the home's value - follow the curve of this upward spiral of the price the house would fetch if it were put up for sale. For many longtime homeowners, especially those on fixed or limited incomes, it doesn't matter if their homes is worth twice what they paid for it because they have no desire to sell. Still they must pay the increased taxes generated by the bullish housing market around them.

The District of Columbia and all Virginia jurisdictions assess private homes on the basis of 100 per cent of the property's value. Maryland assesses private homes on the basis of 50 per cent of the property's value.

Comparisons of what the owners of a similarly priced house in each of the differen jurisdictions pay cannot be made accurately because of differences in the total tax structures.

Using $60,000 as the average price for a home, the property tax a homeowner would pay ranges from a low of $540 in Loudon County to a high of $1,173 in Montgomery County. Generally speaking, the closer the home is to Washington, the higher the property tax.

Despite, the variances, however, officials in all the jurisdictions say homeowners are upset over rising taxes.

William C. Crossman Jr., chairman of the Loudon County Board of Supervisors, said citizens are formally establishing a taxpayers' group in early June.

"They've already let us (the Board) know they'll be very active in the future," said Crossman, the owner of an 800-acre farm in the Middleburg area.

Crossman said homeowners last year sustained assessment increases averaging 30 per cent. This year the Board of Supervisors may levy a increase on the tax rate that could reach 40 per cent. Crossman said, in order to pay for the construction of two new schools and renovation of the county courthouse.

Charles County Administrator Ardath Cade said no increase on the tax rate is expected for the next fiscal year, and there may even be a decrease. The County's current tax rate is $2.42 per $100 of assessed value.

"We're not cutting back any services," Mrs. Cade said of the county's $25 million county budget. "They're being maintained and improved, but without any major additions."

Howard County's $60 million budget, however, may include an increase on the tax rate of up to 19 cents, a county officials said.

"The County Council's working on a 17 cent increase now, and they're trying to get down later," the official said. "They citizens want something trimmed off that 19 cents. They've made that clear."