The Falls Church City Council Monday night approved a second community-operated home for the mentally retarded, permitting use of the 1930s Miller house at 366 N. Washington St. for use by the Fairfax-Falls Church Community Services Board.

The Miller house will become a transitional home for the less than half dozen mentally retarded residents of the nearby city-owned home at 114 E. Columbia St., helping to prepare them to live in the community, said city spokeswoman Barbara Gordon. The city will pay for the upkeep of the Miller house and the community services board will fund the program.

The council voted against creation of a city redevelopment and housing authority, approving instead plans to cooperate with Alexandria's housing authority to assist Falls Church in providing rental housing for moderate and low-income families. A public hearing will be held on the issue Sept. 26.

The council set Sept. 12 for a public hearing on creation of a conservation area to include the Westbrook Gardens apartment complex, to aid the nonprofit Falls Church Housing Corporation in acquiring the complex and preserving the city's stock of rental housing.

In other action, the council:

* Voted an increase of present budget appropriations for four municipal projects: $14,300 for a heating/cooling system for the community center; $60,000 for water main installation and fire hydrants in Langley Oaks; $39,000 for landscape improvements and security lighting at the Cavalier Trail Park; and $25,000 for the water works fund to improve analysis of the city's water flow, pressure and drainage.

* Approved an employment agreement between the city and the new city manager, Anthony Hamlin Griffin. The agreement stipulates that Griffin's term is indefinite as provided in the city charter, that he become a resident of the city no later than July 1, 1984, and that he receive an annual salary of $52,000 plus moving, automobile and general expenses.