Kenneth Back, the District of Columbia's chief tax official for nearly a quarter of a century, will retire next month. Mayor Marion Barry announced yesterday that Back will be replaced by city Treasurer Carolyn L. Smith.

Barry also announced at a news conference the selection of Audrey Rowe, his special assistant for youth affairs, to be acting head of the Social Rehabilitation Administration, the section of the Department of Human Resources that deals with family and juvenile matters.

He also nominated Joyce C. Blalock, a Pentagon lawyer, to be the city's first inspector general, responsible for investigating charges of municipal inefficiency and wrongdoing.

Back's retirement will give the Barry administration firm control over the Department of Finance and Revenue, an agency whose honesty has rarely been questioned but is regarded as a bastion of hidebound and sluggish administration.

The department is responsible for assessing and collecting $900 million from sales, income, real estate and a long list of miscellaneous taxes.

Back, who joined the city government in 1956 when it was headed by three commissioners appointed by the president, was not on Barry's "hit list" of holdover officials targeted for removal when the mayor took office last January.

But there were problems.The department's recently adopted policy of stressing the value of land over the value of dwellings in making real estate assessments came under widespread public criticism.

More recently, hundreds -- perhaps thousands -- of taxpayers complained that the department had lost or misplaced forms that had been mailed claiming real estate tax reductions. Back denied departmental blame, but the mayor ws angered by the episode.

Barry announced Smith's appointment as tax chief at a news conference yesterday at which the mayor only grudgingly discussed Back's retirement. He urged reporters to "look to the future," at Smith's selection, and not to raise "irrelevant" questions over Back's departure.

"I was not unhappy with him (Back)," the mayor declared. Of the retirement, he said it was "a mutually agreeable arrangement. He has served this government very, very well."

Back told reporters later that he wrote the mayor in September saying he intended to retire. At the age of 60, he said, he has the 30 years of government service needed to obtain maximum retirement benefits.

Back said he will become executive director of the Institute of Property Taxation, an offshoot of the Council of State Chambers of Commerce, which has headquarters here. His retirement will take effect Dec. 31, but he said he will go on a terminal leave later this month.

Barry said Back's deputy, Leo J. Ehrig Jr., also will retire next month after 30 years of government service. He said Smith would announce his successor.

The nominations of Smith, 36, and Blalock, 49, are subject to City Council confirmation. In the meantime, Barry said they will serve in their newposts in an acting capacity. Rowe's permanent appointment will await an impending reorganization of DHR that the mayor said he would soon propose to the council.

Rowe replaces William W. Barr, who retired last Friday.

Smith has been D.C. treasurer, an office within the Department of Finance and Revenue, since February 1977. In 1969 she became the first black woman certified by the D.C. Board of Accountancy, and from 1967 to 1977 she was audit manager for the accounting firm of Coopers and Lybrand, the mayor's announcement said.