Arlington's crime rate declined by 2.8 percent during the first three months of this year compared with the same period last year, despite an increase in assaults and robberies, county police said yesterday.

The decline is due largely to a sharp drop in the number of reported burglaries, police said.

Crime figures show there were 287 burglaries in the first quarter of 1983, a 30 percent decrease from 409 during the same period last year.

Police credit the decline in burglaries to stiffer prison sentences for convicted burglars and and Neighborhood Watch programs.

The largest increase was in the number of aggravated assaults, up 72 percent from 47 for the first quarter of last year to 81 for the same period this year.

Other significant increases were in motor vehicle thefts, up 16 percent from 105 to 122, and robberies, up 9 percent from 79 to 86. The number of reported rapes increased 6 percent to 16 for this year's first quarter.

Police reported one murder in the first quarter of this year, compared with three in 1982.

Current figures also show that police improved their crime-solving rate, clearing 29 percent of the crimes reported, compared with a 26 percent rate for the first three months of last year.

Fairfax County, the only other area jurisdiction to report 1983 crime statistics, last week reported a decline in crime during the first quarter of the year.