A study commission charged with the politically sensitive task of recommending whether to build a prison in the District will hold its first meeting today amid indications that its 15 members have widely differing views on corrections policies.

Several commissioners said yesterday they have "mixed feelings" about building a prison to relieve overcrowding at the D.C. Jail and Lorton Reformatory, and were "not convinced" a new facility is needed. Others said they favor adding cells and have no qualms about placing a new institution inside the District line.

"I am trying to approach this with an open mind, without any preconceived ideas," said Joslyn N. Williams, president of the AFL-CIO's Metropolitan Washington Council, a member of the Corrections Facility Study Commission. "In a perfect world, I would not like to see any prisons."

The matters before the commission, Williams said, are complex corrections issues that have eluded experts for decades. Should the commission propose construction of a prison, it must also recommend the type and size of the facility, how to pay for it and where to locate it. "I am not happy with the fact that we have been asked to undertake the monumental task and find an answer in six months," Williams said.

Commission member Margaret Nolan, executive director of the Washington Correctional Foundation, said she is "by no means convinced" of the need for a new facility. She called for a detailed study of the District's inmate population to determine whether alternatives to incarceration are appropriate.

The commission, named Tuesday, was established by emergency legislation passed in response to the surging inmate population within the D.C. Department of Corrections. Mayor Marion Barry, reversing his long-standing opposition to building a prison in the District, announced this spring he favored such construction so long as the federal government provided the funding.

The commission consists of seven mayoral appointees, including Williams, and eight members appointed by City Council members, including Nolan. The panel, faced with a Jan. 19, 1986, deadline, also must consider alternatives to building a prison, including renovating and expanding existing structures.

Barry, during his press conference Tuesday, said he had difficulty finding citizens who would agree to serve on the panel because of the divisiveness of the issue. He said he expects the commission to produce a majority report and a dissenting minority report as well.

The commission is advisory and its recommendations are not binding on the mayor or the council. Subsequent action by District officials could be clouded by early maneuvering for the 1986 election. Corrections policy is likely to be a major issue in the mayoral and City Council races.

"I have great reservations about putting [a prison] in the District," said William P. Lightfoot Jr., a commission member appointed by City Council member Wilhelmina J. Rolark (D-Ward 8), the council's most adamant opponent of a new prison.

Cedric Hendricks, an aide to Rep. John Conyers (D-Mich.) and a mayoral appointee to the commission, said he sees "a need for a new prison because it is clear that the overcrowding . . . necessitates it. The District needs a prison in the District."

Sheila Basey, a commission member appointed by the mayor who is vice president of the Self-Help Center for Female Ex-Offenders, said she has "mixed feelings" about building a prison. Her organization, she said, has always supported alternatives to imprisonment but, she added, "If there needs to be more space provided, we have to accept the fact that that's necessary."