District of Columbia families have the dubious distinction of shouldering the heaviest tax burdens of any residents in the Washington metropolitan area.

Second, third and fourth places go to Prince George's County, Montgomery County and Alexandria, according to a study of state and local tax burdens in 1976 for a family of four in the metropolitan area.Other jurisdictions included in the study are Charles County, Md., and Arlington, Fairfax, Loudon and Prince William Counties and Fairfax City in Virginia.

Taxes on income, real estate, sales and motor vehicles cost District families more last year than other area families, except those in the $5,000 and under annual income category, according to the report, which was released by the D.C. department of finance and revenue.

Another finance department study, entitled "Tax Facts, Fiscal Year 1977," shows that D. C. Residents with incomes over $10,000 pay the highest income tax rates in the area. On incomes of $25,000 or more, the rate is 47 per cent higher than in Maryland and 91 per cent higher than in Virginia.

The 5 per cent D.C. sales tax is also highest in the area now, but Maryland's sales tax will increase to 5 per cent next month. That will leave Virginia, at 4 per cent, a sales tax bargain.

Northern Virginia emerges in the family tax burden study as a relative tax haven for families with incomes of $10,000 and over, except those who live in Alexandria. Combined income, real estate and sales taxes are generally lower in Virginia. Prince William and Loudon Counties have the lowest tax burdens of all.

A spate of D.C. tax hikes last year pushed families in the $10,000 category from fourth to first place among the 10 jurisdictions in 1976. Last year D.C. boosted taxes on individual income, restaurant meals, alcoholic beverages served by the drink, cigarettes, gasoline, automobile titles and registration and deed recordation.

In contrast to better-off families, the position of poorer D.C. families actually improved in 1976. Their tax burden fell from fourth place in 1975 to fifth place last year. They now pay lower taxes than their conterparts in Alexandria, Fairfax County, Fairfax City and Arlington County.

The finance department study shows that the total tax burden gets lighter for families located farther from the nation's capital. For example, in the posh hunt-country of Loudoun County, Va., residents with incomes of $10,000 paid an average of $742 in the combined taxes last year, $250 less than the $992 paid in D.C. In close-in Alexandria, however, residents paid an average of $48 less than in D.C.

As income rise, the differences increase between taxes in the outlying counties and close-in areas. Loudoun County residents, with income of $40,000 averaged $3,000 in 1976, a striking $1,429 less than the $4,521 paid by District families.

Comparisons of the tax rates that affect the family pocketbook are contained in the D.C. finance department's tax facts booklet. This report shows that, contrary to popular opinion, D.C.'s property tax is not the area's highest. It is third from the top, closely following first and second-ranked Montgomery and Prince George's Counties in Maryland. Property taxes are lowest in Loudoun County, Va.

Besides its 5 per cent general sales tax, D.C. also has a high 8 per cent tax on hotels, motels and restaurant meals, and a whopping 12 per cent tax on parking.

The District's new vehicles registration fee - one of the highest in the nation - places it second only to Virginia in total taxes paid on motor vehicle-related assessments. D.C.'s fee for the heaviest vehicles - 4,000 pounds - is $96, more than double Virginia's top of $45 and more than triple the $30 fee in Maryland. D.C.'s fees are scheduled to come down next year, according to the finance department.

D.C.'s taxes put the city in or near the top of the nation's 30 largest cities for tax burdens on upper income families, according to a finance department report entitled "Tax Burdens in Washington, D.C. Compared With Those in the Nation's Thirty Largest Cities, 1975."

The report covers income, real estate, sales and auto taxes for a homeowning family of four with income in selected tax brackets - $5,000, $10,000, $15,000, $20,000, $30,000 or $40,000.

D.C. stood ninth in the nation for tax burdens on the $40,000-income class. New York City led the nation, with a 20.1 per cent tax burden. It was followed by Buffalo, 15.4 per cent; Milwaukee, 14.7 per cent; Boston, 14.6 per cent; Los Angeles, 13.5 pr cent; San Francisco, 12.6 per cent; San Diego, 10.6 per cent; Detroit, 10.3 per cent; and Washington, D.C., 10.2 per cent.

D.C. ranked 17th for families in the $5,000-income bracket. They paid 8.8 per cent of their incomes in taxes, an average of $441 per family. First ranked New York City taxpayers in the same income category paid a startling $1,005 - or 20.1 per cent - as a result of New York's proportional tax system.

In 1975, 292,831 D.C. residents had income tax liabilities, out of a total population of 711,500. Of them, 79 per cent (232,153) had adjusted gross incomes below $15,000. Their total tax liabilities amounted to $53,102,000, according to a finance department report. The remaining 21 per cent (60,678) with incomes of $15,000 and over paid a total tax of $86,009,000.