The D.C. City Council yesterday took the first step toward relaxing city laws that have blocked the establishment of sidewalks cafes in esidentially zoned neighborhoods.

The Council gave final approval to new legislation that would allow outdoor cafes in such areas with the approval of the city's Board of Zoning Appeals and the residents in the area where the cafes would be located.

Previous city law had flatly forbidden such cafes in areas zoned "residential" or "special purpose." The zoning board must still pass new zoning regulations to complement the law approved yesterday.

Efforts to overturn the old legislation, which some had termed "antiquated," began last July, following unsuccesful efforts by proprietir Bosko Millimic to extend his Cafe Lovcen, at 2132 Florida Ave. NW., onto the sidewalk in front of it.

after Milinic had renovated the outside to become a sidewalk eating area, he was denied a permit to carry out which the cafe is located is zoned resi-business there because the area in dential.

The Council also approved yesterday a plan to carry out an "inquiry" into hiring ans contracting practices in several city agencies, including the troubled Department of Human Resources.

The $141,423 plan is a scaled-down version of a more ambitious, $700,000 proposal to investigate city leasing and hiring practices that had been developed in the water of published allegations of widespread mismanagement and leasing and contracting abuses in DHR.

Plans for a costlier, more detailed probe were scuttled when Council numbers changed their attitudes, following preliminary city will report that found by hard evidence of some of the improprieties alleged in newspaper article last fall.

The Council set a spending ceiling of $150,000 and even amended the title if the bill to delete the word "investigate," and substitute the word inquiry. Instead of a stuff of 21 persons, as originally proposed, the inquiry will have nine persons.

Council Member Wilheilmina J. Rolarke (D-eight) was the only one to vote against the plan yesterday. "This is something with a new name that's still playing the same game," she said, "investigation, investigation, investigation," which she wanted to dropaltogether.