When R.C. Courtney moved in 1969 into Crystal Tower North, on South Eads Street in Crystal City, he joined what seemed to be a convenient and safe bedroom community.

"In 1969, we had virtually no crime. You could walk on the streets and feel safe," Courtney said. Since then, Crystal City has gained 5 million square feet of office space; the concrete skyline of office buildings, hotels and condominiums juts 20 stories above the street, and shops line several levels underground.

The number of office workers in the area has jumped by 27,000 since Courtney moved in, and county planners estimate that 43,000 people work in the high-rise offices each day.

With the crowds have come crime rates that many tenants and workers say have injected a dose of urban uneasiness into the once-quiet area.

"Everyone I know knows of some incident that's occurred," said Courtney. "Now, I dare not walk on the street, because I'm going to get mugged."

Police statistics show that, for all but one year since 1978, the census tract that includes most of Crystal City has recorded the highest number of serious crimes in Arlington County. In 1980, the Rosslyn area had more crimes.

About two-thirds of the crimes are larcenies, police say -- thefts of calculators, typewriters or purses from the hundreds of offices that line the Jefferson Davis Highway corridor, Crystal City's main thoroughfare. But in fiscal year 1985, the area ranked second among 38 census tracts in the number of robberies and motor vehicle thefts.

The most recent incident to alarm Crystal City tenants and employes was the robbery and fatal stabbing Nov. 29 of a U.S. Environmental Protection Agency worker on the 11th floor of her office building at 1921 Jefferson Davis Hwy.

There have been other, less violent crimes, such as a rash of more than 100 auto break-ins between January and May of this year.

In January, someone broke the trunk lock of Courtney's 1977 Lincoln, parked in a secured underground garage, and stole more than $2,000 worth of tools and other equipment. Thirteen other cars in the garage were broken into at the same time.

Starting tomorrow, Arlington police hope to halt some of the crime in the area. Deputy Chief David Reiten said one additional officer will patrol in Crystal City during the day and from midnight to 8 a.m.; two officers will be added during the high-crime shift of 3 to 11 p.m. An additional "floating" officer, who may assist those in Crystal City, will be added to each shift.

"We want to prevent crime by our visibility; it's our response to what we see as an increase in street type of crimes," Reiten said.

The recent slaying of EPA employe Linda M. Billings, 45, jarred employes who previously had felt safe in the area and prompted stiffer security in the building where she worked.

"Until Linda was murdered . . . . people generally regarded this as a pretty safe environment," said Steven Schatzow, director of EPA's Office of Pesticide Programs, where Billings worked. "There was some looting, thefts from the offices, but people felt safe going to get their cars, walking around on the street at night."

Since Billings' death, Schatzow said, building security has been stepped up. Employes must show IDs to enter the building after 4:30 p.m.; previously, there was free access until 6.

Elevators from the basement have been programmed to stop automatically at the lobby after 4:30, Schatzow said.

Despite such security devices, installed in many Crystal City buildings along with computerized key cards for garage access, some workers said they continue to worry about crime.

"When I get here early in the morning, I'm very scared to get out of my car if I'm parked down in G-1 or G-2" underground levels, said Barbara Moore, a clerk for the Patent and Trademark Office. "I don't feel very secure at all, especially around holiday time."

Police say crime rates typically rise before Christmas, as thieves target shoppers who they assume are carrying large amounts of cash or credit cards.

"The business of the purse snatcher is much more lucrative this time of year," Reiten said.

Police, residents and landlords in Crystal City say some security problems there have no season. With high-rises above ground and with Metro, shops and garages beneath, the area to be patrolled multiplies vertically as well as horizontally with each new building.

In the "concrete canyon" that sprawls along Jefferson Davis Highway, "traditional police patrol is a thing of the past," said Reiten. "You don't work on a horizontal plane anymore."

While some tenants and workers criticized what they termed lax security, police and building managers pointed out that a lack of street level activity, heavy traffic and convenient access by Metro and car make Crystal City particularly hard to patrol.

In some cases, they said, goals of convenience and security clash; the planner's dream can become the police officer's nightmare.

"In Crystal City, you can travel laterally on four or five different planes," said Reiten. "In some places with underground parking lots, you can go on foot from point A to point B, but not by car . . . . Five to seven minutes after a crime is committed in Crystal City, a suspect could be in D.C., Maryland or elsewhere in Virginia."

And because high-rise construction brings a flood of transients to the area -- construction workers, couriers and job applicants as well as new employes and residents -- a would-be criminal can easily blend in, police said.

"It's not an area where people know each other, where they are looking out. They don't know who belongs and who doesn't," said Sgt. Dan Boring.

Courtney said that even as a longtime resident he recognizes few of the people who stream through Crystal Tower North each day. "People move in and move out. You simply can't keep track of the faces."

"There's a great deal of difficulty in controlling access to those public buildings," said a security consultant to the Charles E. Smith Co., which owns and manages numerous Crystal City buildings.

And the responsibility for controlling access varies with the turf. Many residence managers hire security guards to watch their apartment lobbies after dark; in federal buildings containing classified material or in restricted areas, the Federal Protective Service handles security. Metro police watch the tunnels and trains; Arlington police patrol everything else.

Arlington planners, having seen the crime rise with the concrete towers of Crystal City, are trying to thwart similar crime increases in the fast-growing Ballston area.

Thomas C. Parker, the county's chief of economic development, said police are now asked to review new site plans and make suggested changes in design to reduce crime risks. In plans for Ballston and the Court House Metro area, Parker said, the county is stressing mixed-use development -- a blend of offices, stores and apartments aimed at keeping pedestrian traffic up and crime down