Alexandria Mayor Frank Mann's bid to bring a Class A minor league baseball team to the city has sharply divided Alexandria's two top governing bodies, with the City Council generally favoring the proposal and the School Board opposing it.

The problem is that Mann has proposed that the team, which would be a member of the Caroline League, paly its home games at a field adjacent to Cora Kelly Elementary School and use some of the school's facilities.

But the City Council and The School Board cannot even agree on which body actually owns the playing field and thus has a right to approve its use.

Assistant City Attorney Terrence Cooke said he is currently researching land records to try to determine who owns the playing field.

With only Vice Mayor Nora O. Lamborne in opposition, the council seems set next week to approve $200,000 in city funds for improvements at Cora kelly and to recommend that the board lease the facility to the city so it can be used by the team.

But of nine school board members only two, Michael Mulroney and Wilfred Smith, said in interviews with The Post tht they are in favor of leasing a portion of the school and playing field to the city. Four other members say they are opposed to such a lease while another two say they are leaning against the proposal. Board Chairman Carlyle C. Ring says he has not made up his mind on the issue.

Mann's attempt to bring a team to the city has aroused fears from residents of Lynhaven adn Arlandria, the areas served by Cora Kelly is located the school at 3600 Commonwealth Avenue, that the presence of a team would reduce the chances of reopening the school, which has been closed since June 1976 because of periodic flooding problems. The school board has committed itself to consider reopening Cora Kelly as a school once the flood problems are solved.

"They don't believe the mayor because he's said a lot of different things in a lot of different places" about the baseball proposal, school board member Lou Cook, a strong opponent of leasing the Cora Kelly facilities, said of the community's reaction.

Mann has promised to support the use of more police officers in the Lynhaven area and has said he would support money for the school board to reopen Cora Kelly once the current flood-control program along Four Mile Run is completed.

Some critics of Mann's proposal also have questioned the fact tht no financial supporters of the team have been identified. Mann has said he is not now a financial contributor of the team, but has not ruled out becoming an investor in the future.

The Alexandria Office of Management and Budget has estimated that it would cost the city more than $200,000 in improvements for the field and other items, such as parking, if a Class A team is to play in the city. Mann says the figures are inaccurate in that the largest single item, $120,000 for parking, is unnecessary because an unnamed club supporter is willint to provide it for free.

Most of the $200,000 would have been spent by the city anyway over the next three years for improvements in the Lynhaven area. But if team comes to one city, the money would be spent between now and April.

"It's probably the first time that I'm aware of that the city has been asked to subsidize a private enterprise and use public facilities to do so," said school board member Claudia Waller. She said she was leaning strongly against letting the team use the Cora Kelly facility.

Some school board members said they fear that if they refuse to let the team play at Cora Kelly the City. Council could cut back the board's annual budget request when it eaches the council later this month. Although other counil members denied this, council member Donald C. Casey said that is the school board chooses to "act irresponsibly (on the baseball issue), they're going to have a lot of trouble, a lot of trouble."