The Virginia Housing Development Authority yesterday left the fate of a controversial public housing project in Fairfax County up to the county Board of Supervisors.

The authority said it would give final approval Jan. 11 to a $4.5 million loan to build the 100-unit town house development, called Rolling Road Estates, unless the Board of Supervisors votes against the project before then.

The project is planned by Housing Affiliates, Inc., of Pittsburgh on a 35-acre site on Rolling Road south of Springfield. Some Rolling Road residents near the site have been fighting the project since October. Fairfax Board Chairman John F. Herrity joined two of those citizens in filing a suit against the county planning commission last Friday to prevent construction of th e project.

Herrity and the others claimed that the commission should have acted on the project, but did not. The county housing authority approved the project.

The state authority decided to gibe only tentative approval to the project after Herrity asked the agency to defer action of Rolling Road Estates until the Fairfax Board reconsiders the matter at its Jan. 9 meeting.

The authority said it would make the loan "unless the authority is" told by Fairfax that the "proposal does not conform with the goals and objectives of the housing assistance plan of Fairfax County."

The Fairfax Board voted against the project Nov. 14, but rescinded that position a week later after the federal Department of Housing and Urban Development threatened to cut off $3.7 million in federal community development funds if the county continued to oppose the project.