ACCORDING TO POLICE statisticians, serious crime in the District of Columbia increased six percent in the third quarter of this year over the same period last year. This news is disappointing, since it marks the end of a 22-month period of declining crime reported in the city. And, as one might suspect, there are no simple explanations for this change.But it does help to know what is included in the serious-crime category, which crimes contributed most to the increase, and where in the city the crimes were occurring. The crimes in this category also have varying relationships to citizen fear: homicide, rape, robbery, aggravated assault, burglary, larceny and auto theft. Also, the geographical pattern of these crimes was uneven; it ranged from a reported overall increase of 12 percent in the commercially expanding Second Police District west of Rock Creek Park to a decrease of 6 percent in the Seventh District in far Southeast.

Significantly, much of the statistical increase involves crimes of a nonviolent nature. Reported auto thefts showed the greatest increase - 31 percent. Police Chief Burtell Jefferson attributes this jump from 702 to 920 stolen cars in part to an "increased sophistication" of thieves, who have learned how to circumvent the sterring-column locking mechanisms. Another nonviolent category, reported burglaries, went up 12 percent, from 3,259 to 3,644; this stems largely from break-ins at new office-building developments throughout the city, says Chief Jefferson, notably in the Second District. Reported larcenies were up 2 percent. And reported homicides, which tend to be cases involving acquaintances and families, increased 18 percent, from 51 to 60. More worrisome are the increases in reported rapes, 9 percent, from 100 to 109, and in reported robberies, 4 percent, from 1,544 to 1,602. Even though Washington continues to have a lower rate of violent crimes than many cities, including San Francisco and Minneapolis, that is little comfort to the victim of a violent attack.

The difficulty is in stopping the crimes - something even the best police department cannot guarantee. Sometimes effective law enforcement on one front can contribute to an increase in another kind of crimes. For example, some police experts believe that recent reduction in the supplies of narcotics has meant weaker heroin, and more robberies and burglaries to support more purchases. Also, there are other statistics that come onto play: Unemployment among black teen-agers, for example, increased from 32.9 percent in August 1977 to 48.5 percent in August this year.

Some of the elements that seem to account for the increases, in other words, are beyond the power of the community to control. But there are things that can be done. Chief among them is the continuation of Chief Jefferson's drive to recruit, train and keep more top-flight police officers.