Without a word of debate, the D.C. City Council voted yesterday to revamp the city's real estate tax system by collecting the taxes at three different rates instead of two.

The council also voted preliminary approval of a bill that would prohibit smoking in retail stores and D.C. government assembly rooms. The measure is a much watered-down version of one that received similar preliminary approval by the council last year, only to be killed under heavy lobbying pressure from the tobacco industry.

The new tax measure, if signed into law by the mayor, adds a new category to the present year-old system that divides properties generally into residential and commercial categories, with large apartment houses now considered commercial.

For the tax bills that will be mailed out in August, the new third category will include an estimaited 43,000 rented homes and small apartment buildings with up to five units, none of them owner-occupied.

Units in this group will be taxed at a rate-not yet established-that will be between a rate charged for commercial property and a lower rate charged for owner-occupied residential property.

The rates set last year were $1.83 for commercial property and $1.54 for residential property for each $100 of assessed value. Mayor Marion Barry has said he would propose lower rates for both this year.

The new system is expected to reduce a previously anticipated tax increase averaging $183 per unit on the rental units being shifted into the new category. It also is expected to eliminate a potential windfall tax reduction on many large commercial properties.

The new tax system was approved on a voice vote after a brief explanation by John A. Wilson (D-Ward 2), chairman of the council's Finance and Revenue Committee. Starting with next year's tax bills, large apartment houses will be grouped with the new category of rental housing, Wilson said.

The smoking bill was approved by a vote of 11 to 2, with council members Willie J. Hardy (D-Ward 7) and Wilhelmina J. Rolark (D-Ward 8) opposed.

The council also upheld Barry's veto of a bill that would have permitted advertising on taxicab roof-tops. The vote was 8 to 5 to override the veto. Nine votes were needed to override.

Those voting to sustain the veto were: Wilson, Hilda Mason (State-hood-At-Large), John L. Ray (D-At Large), Polly Shackleton (D-Ward 3) and William R. Spaulding (D-Ward 5).