Rain started here late yesterday afternoon, soaked the streets during the last evening rush hour of 1981, streaked the windshields of late night motorists and was still falling as midnight struck and 1982 began.

The hours-long rain, which tapped the tops of merrymakers' balloons and soaked through their paper hats, and kept some would-be celebrants from going outdoors, marked a wet end to one of Washington's drier years.

The .38 inches of rain for Dec. 31 measured at National Airport at midnight left the total for the entire year 8.22 inches below the normal yearly figure of 38.89 inches.

Although yesterday's rain brought the precipitation figure for December to within .25 inches of normal, 1981 was afflicted by Washington's driest November ever, during which only .29 inches of rain was recorded, as against a normal figure of 2.90 inches.

1980 was also an unusually dry year, with the precipitation figure 9.58 inches below normal. The driest year ever recorded here was 1930, when the total precipitation was 21.66 inches, the National Weather Service said.

For whatever reason, police dispatchers in jurisdictions across the Washington metropolitan area said the number of automobile accidents reported last night was well below normal.

In perhaps the most spectacular incident of the night, a gasoline tanker truck turned over on its side on I-295 near the Naval Research Laboratory in far Southwest Washington.

Thousands of gallons of gasoline were reported spilled on the roadway, and police closed the road between the Woodrow Wilson Bridge and Pennsylvania Avenue SE.

Authorities reported no injuries or fire and the cause of the accident was not immediately known. Efforts to clear the road were reported continuing early today.

The rain that soaked the city last night was expected to end by this morning, as the storm system that brought it moves up the Atlantic Coast. Skies, at least in the early part of the day are expected to be clear, with temperatures rising into the 50s before colder weather arrives.