The District school board got two clear messages on the choice of a new superintendent last night: The next schools chief should be from the city. And the new chief should be from outside the city.

"You two should meet and discuss this, and when you do, I'd like to be there to watch," at-large board member David Eaton told speakers who argued opposite sides of the point.

The hearing at Dunbar High School attracted five speakers and an audience of 31. It was the only opportunity for citizens to tell the board what kind of person should succeed Floretta McKenzie, who announced Aug. 28 that she will leave the school system this winter.

Board President R. David Hall (Ward 2) has pledged to have a new superintendent on the job before McKenzie leaves. However, in the timetable for the 13-member search committee, a list of finalists would be presented to the board by March 30.

The only candidate mentioned by name last night was that of Deputy Superintendent Andrew Jenkins, a former principal whom two speakers supported. Jenkins has told friends he wants the job, but several board members say he is not among their top choices.

The only divisive issue last night was whether to mount a nationwide search or stick to local candidates.

"We need someone whom we know," said parent Goldie Johnson. "I don't want to have to learn about someone else. I want to raise hell with someone I know."

But spokesmen for Parents United, an activist group, argued that an outsider would help the school system destroy perceptions that personnel decisions are based on favoritism.

"If the person comes from completely outside the school system, it would be more likely that perceptions of unfairness could dissipate," said Delabian Rice-Thurston, director of the group. She said the new superintendent should be someone who believes in a parent role in evaluating principals and teachers.

Jay Silberman, a chairman of Parents United, asked the board "to cast our net as broadly as possible. Look all over the country." In an apparent reference to McKenzie's reputation as a thin-skinned administrator, Silberman said the new superintendent should be a skilled public communicator who is "comfortable and not sensitive to the board's criticism."

Board members seemed split on the local-national issue.

"I am looking for the best person and I don't care if the person is inside or outside the system," Eaton said.

"We do have people who are prepared to do the job, if they're given the chance," said Nate Bush (Ward 7). "Our experience . . . suggests there may be difficulties in bringing someone in from outside." He spoke of Barbara Sizemore, a superintendent who was fired in 1975 after a stormy tenure. Sizemore had been hired from outside Washington on the advice of a search firm.

Advertisements soliciting candidates for the $85,000-a-year job will begin running in local and national publications this month.