When Jean Marie Leavy, 51, was shot during a mugging in the parking lot of an apartment complex on the south side of Richmond late Saturday night, she became the latest addition to the longest list of homicides in Richmond's history.

As of yesterday, 96 persons have been slain in 1985, compared with 76 in all of last year, said Richmond homicide Detective W. Ray Williams. The previous record number of slayings in one year was 88 in 1972, according to police records.

"We can't get the [homicide] notices up on the board fast enough," said Williams. "On Nov. 4, four were killed one night . . . . People ask us what can they do. But there are so many variations, the same people are not killing them all . . . . Some are because of arguments, some drugs."

The week between Christmas and New Year's is "usually our busiest time," said Williams. "And this year has already been our busiest in history."

In 1984, Richmond, a city of 224,000, had the fifth highest per-capita homicide rate in the country, according to the FBI's Uniform Crime Report. Judging from the preliminary numbers of homicides in the four cities that topped the 1984 homicide list, Richmond could climb even higher on the list in 1985.

In Gary, Ind., which had the highest 1984 per capita homicide rate, there were 18 fewer killings as of Dec. 27, or 63 in the city of 148,000.

In second-ranked Detroit, the number of killings did rise considerably with 161 more homicides this year, bringing the total as of Dec. 27 to 675 in a city of 1.13 million.

In third-ranked Miami, 35 fewer people had been killed as of Dec. 27 compared with last year, for a total of 135 homicides out of a population of 401,000.

And in fourth-ranked New Orleans, there were 54 fewer slayings as of Dec. 27, or 160 in the city of 576,000.