The Falls Church Board of Zoning Appeals early today rejected a city proposal to allow a group home for troubled teen-age girls in an area whose residents were mostly adamantly opposed to the project.

The board voted 3 to 2 to deny a special use permit to the city to operate a residential counseling center at 407 Little Falls St., a vacant house owned by Shefer Schools Inc.

Neighbors of the house have attended numerous hearings during the last two months to fight the proposal. They argued that a group home would bring a rise in crime and a decline in property values and gave city officials a petition with about 300 signatures opposing the plan.

"I feel this would have an adverse effect on the neighborhood," said board Chairman Charles Vernon. "The peace and the safety of the individuals living next to this home ought to be considered."

Falls Church will no longer be able to house delinquent girls in a home in Fairfax County after Jan. 1, when Falls Church withdraws from the 19th Judicial Circuit, which includes Fairfax County and Fairfax City, and merges with Arlington in the 17th Judicial Circuit.

Falls Church's delinquent boys will be eligible to enter Arlington's Argus House, and city officials had proposed that Falls Church house delinquent girls.

The house on Little Falls Street would have been renovated and used to serve up to 12 girls, aged 13 to 17. The girls, the majority of whom would come from Arlington, would be referred to the facility by the Juvenile Court and would include runaways, habitual truants, abused or neglected teen-agers and delinquents convicted of minor crimes.

City Manager Anthony H. Griffin said city officials will seek another site in the city for the home.