Residential property values increased 21.4 percent in the District of Columbia during the past year, the D.C. Department of Finance and Revenue announced yesterday, pushing the worth of a typical city dwelling to nearly $86,000 and setting the stage for an increase of $165 on the average real estate tax bill.

The largest increases occurred in Foggy Bottom and the Southwest urban renewal area, where revaluations of cooperative apartment units in buildings that once were rental properties pushed the average rises more than three times the citywide rate.

Elsewhere in the city, the greatest proportionate increases took place in two older areas on the northwest fringes of downtown -- Kalorama, with a 39.3 percent rise and an average valuation of $235,000, and Mount Pleasant, with a 37.1 percent rise and an average vaulation of $103,570.

The smallest increases occurred in three neighborhoods east of the Anacostia River -- Randle Heights, up 5.3 percent to an average of $43,410, Deanwood, up 5.4 percent to $37,504, and Hillcrest, Mayor Marion Barry's neighborhood, up 5.6 percent to $67,066.

According to the tax assessors, the most expensive neighborhood is Massachusetts Avenue Heights, the area north of that thoroughfare between Rock Creek Park add the Washington Cathedral, where the typical home rose 24 percent in value to an average of $324,140.

The least expensive is Barry Farms in Southeast bordering the north side of St. Elizabeth Hospital, where values rose 7 percent to an average $34,157.

For the first time in memory, tax valuations on commercial property -- chiefly stores and office buildings -- increased more steeply than they did on residences. Commercial valuations increased 25.1 percent, adding $1.4 billion to the city's total value for tax purposes, while the overall 21.4 percent in residential values added $1.2 billion to the tax base. A third category or properties, large rental apartment buildings, went up 18.6 percent in value, adding another $800 million.

Over all, the new assessments will bring the city's total property tax valuation to a shade under $18 billion. Formal notices of the new assessments were mailed out yesterday to all property owners. The assessments are subject to appeal, which could reduce the figure somewhat.

Legally, the assessments will not result in tax increases automatically, since the mayor must first recommend to the City Council the tax rates to be applied to the new valuations, and the council then must set the rates on which the tax bills will be based. In recent years, tax bills have risen at about the same rates as the valuations.

If that happens again, which seems likely, the taxpayer, who paid $77.3 in the 1980-81 tax year on the average assessment of $72,372, can expect to owe $938 in 1981-82 on the higher assessment of $76,920 -- an increase of $165. Taxes are due in two annual installments.

The new tax calculation is based on keeping the current tax rate of $1.22 per $100 of assessed value on single-family residential property, including condominium and cooperative units, and taking advantage of an exemption of $9,000 in assessed valuation the city grants to homeowners occupying their own property.

Unlike most jurisdictions, the District levels separate tax rates on different types of properties. The rate on commercial property is $2.13 per $100 of valuation, and on large rental apartments it is $1.54 per $100. Suburban jurisdictions have one rate for the different types of property, ranging from $1.12 per $100 in Arlington to $1.64 per $100 in Montgomery County.

The 21.4 percent rise in residential valuations in the District is pretty much in line with the recent trend. The biggest annual increase in the last five years was 25.1 percent in 1976-77, followed in the four succeeding tax years by increases of 19.7 percent, 17.8 percent, 19.3 percent and -- last year -- 22.6 percent.

The finance department's listing of assessments by neighborhoods reflects the fact that values in some popular areas that rose fast in previous years have now stabilized somewhat. For example, values in the city's Chevy Chase neighborhood rose 13.2 percent, those in Shepherd Park rose 15.1 percent and those in Georgetown 17 percent, all well below the 21.4 percent citywide average. Neighborhoods where values rose within a percentage point of the citywide average include Brookland, Burleith, Cleveland Park, Forest Hills, LeDroit Park, Petworth, 16th Street Heights and Trinidad.