UNTIL the Westchester Children’s Museum raises $7 million, plans for it to occupy a historic bathhouse complex at Playland Amusement Park in Rye are delayed, county officials said.

The financial requirement — part of a matching-grant agreement struck several years ago between the county, which owns the bathhouse complex, and the museum — postpones the opening to at least 2010.

Last week, the office of the county executive, Andrew J. Spano, learned that its part of the deal — rehabilitating the vacant structure, which is listed on the National and State Registers of Historic Places — will not only cost significantly more than anticipated, but also must be completed as soon as possible to save the building from further decay.

The initial timetable was to renovate the 1920s bathhouses this year, with the goal of having them ready for the museum by the fall of 2009, said Susan Tolchin, chief adviser for Mr. Spano. She said the dates for renovation were contingent on the nonprofit museum group’s raising enough money to prove it was viable economically, which set back renovations at least a year.

But the county must move quickly to save the building from further deterioration and spend at least $1 million more than anticipated on the project, Ms. Tolchin said. Problems include asbestos and lead paint in the building, which has been vacant for nearly 40 years.

“Whether it becomes a children’s museum or something else, we have to make these repairs, our Departments of Parks and Public Works have told us,” she said. Because the 40,000-square-foot bathhouse complex is designated as historic, as are other buildings at Playland, the county by law must protect it from further deterioration.

Daniel Heuberger, a principal with Richard Dattner Architects, one of the architectural firms working for the museum group, recently warned that the bathhouses’ roof was no longer structurally sound and that the interior had sustained water damage. “Obviously,” he said, “things won’t get better over time.”

The structural vulnerabilities have been exacerbated by recent flooding.

The county had intended to lease 20,000 square feet of the bathhouse complex to the Children’s Museum for 30 years, charging it $1 annually for rent.

The idea for the children’s project, a hands-on museum for youngsters, grew out of a study in the late 1990s and was further developed by a group of young mothers seven years ago who met around their kitchen tables, said Corinne Zola, the president of the museum’s board of directors.

The museum is being planned as a learning center in which children can explore the history, arts, environment and cultural diversity of their own communities, and of others in the county and in the world at large, Ms. Zola said.

Ms. Zola said that the group had to spend $2 million of the $4 million it had raised so far to pay for architectural plans and content development.

The requirement that the group raise about $5 million more to match the county’s contribution is only part of the problem. The Children’s Museum faces other hurdles, including scrutiny from county legislators and residents who question spending taxpayer money on such a project.

“It’s always an issue of how much the county should be spending on an amusement park, and that has come up before the Legislature,” said Judy Myers, a Democratic county legislator representing part of New Rochelle and all of Larchmont, Mamaroneck and Rye. But Ms. Myers, who supports the children’s museum, said that however the bathhouses are eventually used, the county must preserve the building.

Although Ms. Tolchin reiterated that Mr. Spano was committed to the idea of a children’s museum at Playland, William J. Ryan, chairman of the Board of Legislators, said that other “park-related, entertainment-related” uses might be considered.

A Croton-on-Hudson resident, Berl Brechner, questioned the need for public spending on a children’s museum “in a cash-strapped economy” when many other public and private programs were available. He said the money might be better spent to improve and upgrade existing facilities for children.

“I’m not taking a stand against the children’s museum,” said Mr. Brechner, the owner of radio and television stations. “I’m just one voice raising questions.”