Major reported crime in the District of Columbia decreased significantly in the first quarter this year compared to the same period last year, except in commercially expanding areas west of Rock Creek Park where police recorded a near-20 percent jump in shop-lifting and office thefts.

The D.C. Police Department's quarterly statistical report shows a city-wide decline of 5 percent in serious crimes reported to police - from 11,642 offenses in the January-March 1977 period to 11,069 offenses in the same period this year.

But an area-by-area breakdown of the figures shows an overall increase of 7 percent in the 2nd Police District west of Rock Creek Park. There police reported a 19.6 percent leap in larcenies most of which were shopliftings, thefts of office equipment and other commercial thefts.

Rapid commercial growth in downtown and Friendship Heights portions of the 2nd District has apparently contributed to the increase in property crimes, said district watch commander Capt. Roger Roch yesterday.

"We're probably picking up another two or three (shoplifting) offenses a week at places like Neiman Marcus at Western and Wisconsin Avenues," Roch said. "There are a lot of new office buildings going up all over downtown, too. . . As soon as one opens, we start getting reports (on stolen typewriters, calculators and other equipment)."

Second District figures show, for example, that the number of reported larcenies jumped by more than 100 from 415 in the first quarter this year.

The 1st District which, like the 2nd District, embraces much of commercial downtown, also recorded an increase in property crimes, but on a much smaller scale - only 3 percent all the other five police districts in the city reported decreases ranging as high as 13 percent in the 5th and 6th districts of Northeast Washington.

Major crimes are divided by police into seven general categories - homicide, rape (including attempts), robbery, aggravated assault, burglary, larceny and auto theft.

Homicide, rape, robbery and aggravated assault are classified as crimes against persons and showed an overall 12 percent decrease throughout the city in the first quarter, according to the police report.

The statistically much larger category of crimes against property - larceny, burglary, and auto theft - showed a citywide decrease of 3 percent with the 13 percent decrease of the 5th and 6th districts ofofset by an 8 percent increase in the 2nd District.

Police Chief Burtell Jefferson attributed the general decrease to continued effectiveness of "Operation Doorstep," a joint police U.S. attorney's office effort to remove known criminal repeaters from the streets. Jefferson also credited "community involvment" and increased citizen willingness to report crimes and to testify as witnesses.

Citywide, all categories of major crime, expert auto theft, were reported down in the first quarter this year.

Robbery, considered by police officials a key offense in determining possible trends, declined from 1,782 reported cases in the first quarter of 1977 to 1,556 this year, a 13 percent drop.

Reported homicide fell from 50 to 37, rapes from 95 to 72 and aggravated assaults from 571 to 544, according to police figures.

In the property crime categories, reported burglaries fell from 2,672 to 2,620, a 2 percent decline. Total larcenies citywide dropped 5 percent from 5,810 to 5,533.

Reported auto thefts increased 7 percent from 662 to 707.