Three Maryland Democrats seeking their party's Senate nomination came here tonight for their first joint appearance of the campaign, an event disrupted several times throughout the evening by protesters.

Gov. Harry Hughes, who has not announced for the Senate but is expected to run, was scheduled to join the panel but pulled out this afternoon because of the flu.

During the debate, which was sponsored by several Baltimore County Democratic clubs, Rep. Michael D. Barnes of Montgomery County criticized support of a tax credit for private school tuition by Rep. Barbara A. Mikulski of Baltimore. Barnes and the third candidate on the panel, Baltimore County Executive Donald P. Hutchinson, said they were opposed to a tuition tax credit. "My strong view is that the federal government should not be in the business of financing private education," said Barnes.

Mikulski said later that she had supported a tuition tax credit in 1977 and 1978, during the Carter administration, because it was supportive of public schools. She said she would oppose tuition tax credits under the Reagan administration because it would be a step toward dismantling public schools.

Most of the contention of the evening, however, was between Baltimore County Democrats sponsoring the event and two additional candidates who wanted to speak -- Debra Freeman, who is backed by perennial presidential candidate Lyndon LaRouche, and A. Robert Kaufman, who said he is a social activist and former socialist.

Kaufman walked up to the rostrum and said that unless permitted to speak he would have to be removed forcibly and arrested. He was permitted to make a short statement.

Freeman, who has run against Mikulski for Congress previously, was accompanied by a few colleagues who chanted and yelled out throughout the meeting, causing sponsors to cut short the event after only a few questions.

Towson is a suburb of Baltimore, and Barnes acknowledged at the outset that most of the people in the audience were supporters of Hutchinson or Mikulski.

"I know a lot of you aren't with me tonight, but I hope by September you'll give me some consideration," Barnes said. He compared his situation now to that in 1978 when he was first running for the House and was far behind in the polls. He won that race, and in 1984, he said, he received 50,000 more votes than Mikulski got in her election victory that year.

Barnes noted that he had been endorsed Saturday by the Jesse Jackson-inspired Rainbow Coalition and today by a dozen Hispanic leaders, and he said he is "the only candidate in this race with a broad base of experience in the issues that will face the Senate . . . . "

Mikulski said she had concentrated on "bread and butter" issues while in Congress, such as jobs, the Baltimore port and a professional football team for Baltimore.

Hutchinson said his experience as a county executive who had to administer a county budget gave him a better background to solve federal fiscal problems.

He said decisions are often made in Washington "without any thought to impacts back home" and that voters should send to the Senate "people that are in the business of budgets and balancing."