Crime in Fairfax County fell by 21 percent for the first half of 1982 to a six-year low, according to police figures released yesterday.

A number of major crimes, including murder, rape, robbery, aggravated assaults, burglary, larceny and car theft, fell to 10,954 offenses for the first six months of the year from 13,846 for the same period last year.

The decline was paced by a steep drop in burglaries, to 1,882 this year from 3,295 in 1981. The total represents the lowest first-half burglary figure since before 1975, according to police.

Col. Carroll D. Buracker, Fairfax County chief of police, attributed the decrease to good police work and citizen cooperation. "We are proving property crimes can be deterred and prevented," he said. "It is no coincidence that during this . . . period the number of Neighborhood Watch groups in Fairfax County passed the 250 mark." Such groups, formed in cooperation with police, are designed to prevent crime by increasing vigilance in a neighborhood.

Besides murders, which held steady from last year's first-half figure of three, and aggravated assaults, which increased from 161 last year to 164 this year, all other major crimes in Fairfax dropped in the period ending June 30.

The number of reported rapes fell to 46 compared with 61 last year, and the number of robberies was down to 241 from 274.

Among property crimes, besides burglaries, larcenies were down to 8,013 from 9,243 last year. The larceny fgure was the lowest since 1978. Motor vehicle thefts fell to 605, the lowest figure since before 1975.

Fairfax City also reported earlier this month that crime went down sharply for the first half of 1982.

Buracker, especially pleased by the drop in burglaries, said "We have regarded burglary of our citizens' homes as our biggest crime problem."