Potomac residents, fighting a proposed trash landfill with the argument that the scavenger birds attracted to the site would be a hazard to planes landing at Washington National Airport, won their battle yesterday when the state refused to grant a permit for the site.

Montgomery County, unless it prevails in an appeal of the state ruling, is now left with only one possible landfill site in Laytonsville, and that site is already under attack by some residents there.

The state Department of Health and Mental Hygiene ruled yesterday that issuing a permit for the Potomac site would compound an existing danger to human life posed by birds in the flight path of planes approaching National Airport.

The site at Persimmon Tree Road and Bradley Boulevard, about 10 miles from National, is "located under a heavily trafficked jet aircraft arrival and departure route," according to a state hearing officer who presided at public hearings on the proposed site.

The Federal Aviation Administration has pointed out that birds can cause an airplane crash if they fly near enough to be sucked into its engines.

Montgomery County officials are "in a race with the clock" to meet a state deadline to build a new landfill by 1981 when the current Gude-Southlawn landfill reaches its capacity, according to county environmental planner Andrea Weirich. After the site is chosen the county still must aquire the land, design the landfill and construct it, Weirich said.

The county "probably will appeal the ruling" on the Potomac site, according to another county official.

The county, in a $22,000 consultants' report on the birth rates, mating habits, diets and mortality rates of 13 local species of birds, attempted to blunt the bird-hazard charges with a conclusion that the proposed Potomac and Laytonsville sites pose "no increased risk" to airplanes.

Hearings on the proposed Laytonsville site, east of Route 108, are going on now, and the bird controversy is threatening to flare again.

Stephen Glassman, a Laytonsville lawyer, said the proposed site is on the flight path of one of the busiest small-craft airports in the nation, the Montgomery Airpark. Glassman also presented witnesses in an attempt to show that pollutants from the landfill could leak into the ground water beneath the landfill and be carried to the Patuxent River basin.

But Weirich said that studies by the county show that ground water leaving the site will be "drinking-water quality." As to the possible bird problem, she said the county's view is that "there is no impact" at the Laytonsville site.

The county already has spent about $2.5 million on what one official called the "most exhaustive search in the country for a landfill site."