Alexandria residents expressed growing apprehension yesterday following the second murder in six weeks in the city's historic Old Town district whose very charm, many of them said, lulls them into a false sense of security.

Police disclosed yesterday that Constance Challenger Mellon, 36, had her hands bound in back of her when she was found Tuesday afternoon in her undisturbed second-story front bedroom, Mellon, a publishing executive Time-Life Books Inc., had been shot once in the head with a small-caliber hadgun inside her tiny but fashionable town house at 406 S. Royal St. in Old Town.

Newly arrived from New York, Mellon had moved into the town house, within easy walking distance to her office, only Friday. Her furniture and personal belongings were still piled in disarray yesterday in her living room.

Officials said they were seeking the owner of a brown Toyota with New York license plates that was seen in the area about the time of the slaying, but police said they had no suspects in the puzzling case.

There were no signs of forced entry and police said robbery did not appear to be a motive.

The fatal bullet entered the left rear part of the victim's head and exited through the right cheek, according to police Lt. Arthur Bratcher. Bratcher said a preliminary autopsy showed no evidence of sexual assault. Mellon's body was identified yesterday by her brother-in-law, Steven Dunham of New York.

The slaying left Old Town residents and Time-Life employes shaken.

"In New York and London and vast cities like that you get used to things like that happening, but you don't expect it when you live in a small, toy town," said Pam Gould, a researcher for Time-Life Books and an Old Town resident for 10 years.

Sandy Danaher, who is opening a new hairdressing shop several blocks from the slaying site, said she planned "to start locking my doors during the daytime. After you've lived in the suburbs all these years, you've got to reevaluate your thinking in the city."

Alexandria crime statistics, which police say have taken a worrisome turn upward, underscore that concern. Last year burgleries and larcenies each increased a dramatic 21 percent in the city, but at a rate that was nearly double that of neighboring jurisdictions. Assaults rose by 14 percent, from 270 in 1978 to 310 last year, officials said.

The Mellon case is the latest in a series of violent deaths in the last two years in the normally quiet Old Town section. In 1978, socialite Donita Curtis was beaten and bound in her historic town house during an apparent robbery attempt, and died from smoke inhalation after an intruder set fire to her house. The case remains unsolved.

Two months ago, an Old Town shop owner, Carol Ann Dodd, was shot in the back and killed during a daylight robbery in her Washington Street optician's store. Two suspects have been indicted on murder charges in that case.

Another Time-Life employe, Mark Chase Sawtelle, was seriously wounded last March after being shot at point-blank range during a robbery attempt near his Alexandria office.

"The impression is that Alexandria is a nice, quiet place . . . [but] we're all going to think twice about going out at night," said Jayne Wise, a Time-Life researcher. Wise said that residents of the area were "upset" about continued crime reports, as were relatives of some of those living in Old Town.

"My mother called me up," she added.

Robert E. Bellavance, head of the city's Chamber of Commerce, said the crimes have caused "much concern, much fear" among the merchants and employes of the growing Washington Street commercial strip that runs through Old Town.

"Many of the businesses are now operating under a locked-door policy. That's no way to exist," he said.

Bellavance disputed suggestions that rising crime might discourage businesses from relocating in Alexandria, a city that prides itself on maintaining its small-town, colonial atmosphere while catering to an increasingly affluent restaurant and shopping clientele.

Time-Life's employes were having the same [crime] problems, only more so, in New York," he said. "But I'm sure they never expected to find anything like that here." However, residents of the tree-lined neighborhood where the quiet, prematurely gray-haired Mellon lived say their peace and quiet has been increasingly disturbed recently by threatening incidents, many of which they say are not reported to police.

"I was walking down the street one evening when three boys tried to grab me," said Sue Lautenbach, a social worker. "I had my keys in my hand and scared them off. Then I ran."

Guerin Todd, a retired lawyer and Pentagon official, said one of his neighbors was beaten during an attempted rape in her town house several months ago. The woman did not report the incident, he said.

"I have a complete feeling of helplessness here," said Todd, who moved to the city's Old Town district 14 months ago. "This is such a charming area, but the police can't seem to do anything about the crime."

At Time-Life offices yesterday, not every employe was taking Mellon's slaying as a warning to be more careful. Bob Menaker, a writer, said he looked at the incident as "just something that can happen. . .. I'd still feel safe in Old Town."

Mellon was so new to the company that "hardly anybody knew her," one employe said. And another noted sadly that a Time-Life worker had been asked by a friend "to look after" the new Alexandria resident. "But he never got the chance."