Serious crime in the District of Columbia has tapered off slightly during the last six months, but the crime rate is still well above the rate a year ago, D.C. police reported yesterday.

Major reported crimes -- murders, rapes, burglaries, robberies, assaults, larcenies and car thefts -- jumped 22 percent, from 13,129 for the first three-months of last year compared to 15,882 for the same period this year.

However, officials noted that the daily average of major reported crimes for the six-month period between October 1980 and March has declined from 198 crimes a day last October to 168 crimes a day in March. That decline is continuing, police say, and on Monday there were 161 crimes committed.

"I think it is significant that the daily average of crimes has been a continual decrease in recent months," said Asst. Police Chief Maurice T. Turner, who released the figures yesterday. "I think the 13-point crime prevention plan is beginning to pay some dividends."

The 13-point crime fighting plan was announced in February by D.C. Mayor Marion Barry and D.C. police Chief Burtell M. Jefferson, who is retiring June 30. The plan calls for increased lighting in high-crime areas, changes in police patrols, use of police decoys and greater participation by the community in solving crimes.

The plan was initiated after the number of reported crimes increased 13 percent in 1980 over 1979. Officials blamed the increased on unemployment, inflatioin, the rising cost of living and the increased availability of herion. i

While turner credited the mayor's anticrime plan for a decline in recent months, some officials said the decrease also could be attributed in part to the fact that some major reported crimes, such as larcencies and robberies, generally drop in the winter, when there are fewer persons on the streets, and increase in the summer.

Turner said he does not believe that crime is that seasonal. Police department statistics for recent years show a leveling off of the seasonal peaks and valleys that were so pronounced in the crime statistics of five to 10 years ago. In the early 1970s, crime was highest in the first three months of each year.

While the daily average of crimes has been declining in recent months, the daily average number of reported crimes for the first three months of this year -- 176 -- was still higher than the 156 daily average in the first quarter of 1980.

According to the figures released yesterday, murders increased 27 percent, from 46 for the first three months of 1980 to 57 for the same period in 1981. Reported robberies jumped nearly 50 percent, from 1,808 to 2,680. Burglaries leaped 31 percent, from 3,183 to 4,122.

Larcenies rose from 6,712 for the first three months in 1980 to 7,291 for the same period this year. Aggravated assaults increased 30 percent, from 622 to 797. Car thefts leaped 26 percent, from 667 to 834, while the number of rapes increased from 91 to 101.