The director of the Baltimore city public housing authority has rejected an invitation to head Washington's troubled and deficit-plagued public housing projects, rebuffing District housing officials in their eight-month search to fill the unpopular post that has attracted few qualified applicants.

Meanwhile yesterday, a group of public housing tenant leaders sent D.C. Mayor Marion Barry a strongly worded petition threatening a possible rent strike and withdrawal of their political support of Barry if acting public housing administrator Sidney Glee, 39, is not appointed to the job permanently.

The position hsa been vacant for two years, but city officials did not start actively recruiting until last October for the $50,000-a-year post. The job entails managing the District's 12,000 public housing units that are home of 1 of every 10 city residents.

Baltimore public housing chief J. Van Story Branch, the first choice for the job, who made at least two trips to Washington to visit several public housing projects, recently told city officials that his wife's illness would make it impossible for him to take the job in the near future.

Washington housing officials said Branch, a Baltimore native who started with the housing authority there in 1943 and worked his way to the top, was also concerned that he would be required under District Law to live in Washington if he took the job. He is nearing retirement age.

Robert L. Moore, director of Washington's Department of Housing and Community Development, denied that the job was ever formally offered to Branch, but sources close to Moore said, "They wanted Van very badly."

But public housing tenant leaders, led by Kimi Gray, president of the Residents Advisory Council, said she believes a selection is imminent.

"We feel that things are being finalized so we want the mayor to know now what we want," Gray said. "Things are being kept too hush-hush and in this city that usually means something's going on."

She led the movement to send the mayor a petition that said, "Our feelings are so strong on this issue that we will not be inclined to lose the vote for you and we will campaign against you among the residents throughout this city. There may also be the possiblity of a city-wide rent-strike."

Gray said she and other tenants supported Glee because he has answered calls in the middle of the night from residents without heat or hot water, distributed stoves and refrigerators on an qual basis, attended meetings of residents when asked and given residents more power in the running of their projects.

It is understood that Chester Thomas, a retired army colonel now studying for a doctorate in urban affairs at Renselae Polytechnic Institute in Troy, N.Y., is also under serious consideration for the Washington job. Thomas, who city officials say has management but no housing experience, also ame to Washington for tours of several projects.

Both Branch and Thomas were reportedly escorted on their tours by Glee, who has applied for the job. Glee was a middle-level bureaucrat in the city's health and welfare department until his old college friend, Moore, made him acting administrator of public housing two years ago.