Alexandria police said yesterday they are still investigating "all areas" in connection with the slaying of Time-Life Books employe Constance Mellon, whose bound body was discovered Tuesday in her Old Town house.

A preliminary autopsy conducted Wednesday failed to reveal the exact time of Mellon's death, they said. She apparently was fatally shot in the head sometime between Saturday and Tuesday, with a small-caliber handgun.

Though police have said they know of no motive or suspects in the killing, they would not comment on the whereabouts of what friends described as "a valuable, antique diamond ring" Mellon usually wore.

Most of her possessions were still in packing boxes when her body was discoverd, police said. Her bed, where the body was found, had been made "as if to sleep in," according to one detective.

Mellon had moved to the area in mid-September after 10 years with Random House publishers in New York, where she lived alone in a Manhattan apartment. For two weeks before her death, she lived in the Old Town Holiday Inn near the Time-Life offices on Duke Street. Police said she originally checked out of the hotel Sept. 30 to move into the small but fashionable town house at 406 S. Royal St., but checked back in shortly after, apparently because her new home wasn't ready.

She finally moved out of the Holiday Inn and into her town house last Friday. Police said she was seen being helped by two men, but said they did not know which moving company handled Mellon's furnishings. They also said a truck and a brown Toyata with New York license plates parked outside the house that day have not been located.

Friends said Mellon's apartment had been burglarized shortly before she moved from New York and that she had received "strange phone calls" last month. They also said she was met at National Airport by a friend from Texas whom she had not seen for a long time, and spent some of her first evenings in Alexandria visting some of the city's restaurants and bars with him.

Police said a preliminary autopsy showed no signs that Mellon had been sexually assaulted, but that more tests would need to be conducted before that possibility could be ruled out and before they could firmly establish the time of her death.

Police said yesterday that officers summoned to Mellon's house on Tuesday found a radio plugged in and tuned to a rock station. A stereo belonging to the woman, described as an enthusiastic rock music fan, was still unpacked.