Democrat Marion Barry yesterday challenged Arthur A. Fletcher, the Republican nominee for District mayor in Tuesday's election, to make public his income tax returns for the last six years, as Barry has done.

But Fletcher refused, saying, "I'm not on the public payroll, so the public has no right to know about my private affairs."

Barry's challenge came during a heated exchange between the two candidates about personal finances during taping of a half-hour debate to be broadcast on the "Black Reflections" show Saturday night on WITG-TV, Channel 5.

The session included some of the sharpest verbal bal infighting of the campaign, which is moving into its final days. According to a poll released yesterday, Fletcher still is trying to make crucial political inroads among the city's dominant Democratic voters.

Ironically, Fletcher had raised the issue of personal finances during what was to have been a program devoted to answers from the two candidates to question sent in by city residents.

Shortly into the program, Fletcher challenged Barry to disclose the contents of a saled envelope, which all elected officials are required to file with the city of Board of Elections and Ethics as part of the conflict-of-interest code.

The contents of the envelope was the subject of a closed door meeting between Barry and elections officials Monday at the District Building. The officials are conducting what began as a routine audition Barry's personal finances.

"You and what's in that file are the issue now, and I don't think the voters are gonna allow you to go any further 'til you explain it," Fletcher said.

Barry did explain it, saying the envelope contained only a copy of a public financial disclosure form, a form inquiring about his ownership of stocks and bonds and the income tax returns he made public in April. "I can say categorically that I don't own any stocks and bonds and haven't received any income from that," Barry added.

Then he challenged Fletcher to disclose his tax forms. "I have no problem with releasing my income tax," Fletcher said. After the debate, however, when a reporter asked for the forms, Fletcher said he meant that he would release them only if Barry allows the sealed envelope to be opened.

Fletcher also proposed in last night's debate that the Public Service Commission, which regulates utility companies in the city, be changed from its present status, as a three-person board appointed by the mayor and confirmed by the city council.

Fletcher called for an elected board, with one member from each of the city's eight wards and one member elected at large. Fletcher said such an arrangement would allow more consumer representation on the board.

Barry said he would oppose that plan, in part because it could allow utility companies to run their own candidates for office and perhaps gain control of the board.