Mayor Sharon Pratt Dixon yesterday appointed Vincent C. Gray, a longtime advocate for the retarded, to head the D.C. Department of Human Services, the city's largest and most troubled agency.

Dixon said one of Gray's first tasks would be to consider dividing the huge department into two agencies.

Gray, who has been executive director of the D.C. Association for Retarded Citizens for 16 years, would take control of city agency next month.

Dixon also appointed Betty Hager Francis, an administrative law judge for the Massachusetts Department of Public Works, as director of the Public Works Department and Maria Gonzalez Borrero, assistant city manager of Hartford, as director of the D.C. Department of Employment Services.

Dixon praised the three new Cabinet nominees as capable administrators who would bring "a great wealth of experience" to their posts. The appointments are subject to approval by the D.C. Council.

In a separate development, Dixon has approved an extra two weeks of police protection for former mayor Marion Barry, according to aides. The extra security, provided by a police sergeant and two detectives, began Monday and will expire on Jan. 21, Dixon spokesman Paul Costello said.

Dixon told reporters that she approved Police Chief Isaac Fulwood Jr.'s recommendation for the extended security because "there had been some legitimate reasons for some concern" about the mayor's safety. She did not elaborate.

In taking charge of the Human Services Department, Gray would assume responsibility for a $1 billion-a-year agency with authority over a wide variety of programs, including Medicaid, Aid to Families with Dependent Children, St. Elizabeths Hospital and public health and drug treatment clinics, as well as services for people who are mentally retarded, disabled or afflicted with AIDS.

The agency has been beset by problems, including mismanagement of hundreds of millions of dollars worth of contracts; numerous violations of long-standing court orders involving services for the homeless, retarded and mentally ill; and a perpetual reshuffling of top managers. During Barry's last term, the agency had five directors. It is being run on a temporary basis by Mental Health Commissioner Robert A. Washington.

The problems have prompted calls for the agency to be divided into two, with a separate Department of Public Health. Council member H.R. Crawford (D-Ward 7), chairman of the Human Services Committee, said yesterday that he plans to submit such a plan in the spring.

At a news conference yesterday, Dixon said one of Gray's first tasks would be to explore breaking up the department "into manageable components." She stopped short of endorsing the step, however, saying she would leave it up to Gray for review.

"The council is enthusiastic about this," Dixon said. "I think we can all work together to achieve a constructive end."

Gray, a native Washingtonian who served as co-chair of Dixon's human services transition team, said that his priorities include straightening out the contracting problem at the Department of Human Services, in which dozens of vendors are operating without formal city contracts. He also said the city might have to reduce benefits, although his first step in coping with the budget deficit would be to scale back the bureaucracy.

Gray, who oversees a budget of $8 million in his post with the Association for Retarded Citizens, has never supervised an agency of the size of the Department of Human Services.

But pointing to his work in his present post, he said: "I've had an opportunity to see DHS close up, not only from the perspective of people with disabilities, but across the board. I think that's an advantage over someone coming from elsewhere to take over this responsibility."

"We can do better than what we've been doing," Gray said of the department.

In Hartford, Borrero worked with the board of education, private sector and neighborhood organizations, according to information provided by Dixon aides. She also was a founder and director of the Hispanic Health Council in Hartford.

Francis joined the Massachusetts Department of Public Works in 1984 as deputy chief counsel and legal adviser to the Public Works Commission. Previously, she served as a lawyer for the Boston Housing Authority. She, like Gray, is a native Washingtonian.