Serious crimes reported last year in Prince George's County dropped 2.6 percent compared with 1976, the second consecutive annual decrease, according to statisics released this week by Police Chief John W. Rhoads.

The overall total was down from 39,578 to 38,544 for murder, rape, robbery, aggravated assault, burglary, larceny and auto theft. In individuals categories, however, murders were up, from 38 to 53 and so were burglaries, from 9,627 to 9,921.

The sharpest drop, 16.1 percent came in auto thefts, down to 2,929 from 3,490 the previous year.

All other categories registered decreases: Robberies, down .4 percent, from 1,941 to 1,933; aggravated assaults, 5.7 percent, from 1,611 to 1,576, and larcenies, 3.2 percent, from 22,591 to 21,868.

Rhoads, at a press conference, attributed part of the drop to an overall 11 percent decrease during December, when administrative and support police personnel were added to the street work force.

The 39.4 percent increase in murders could not easily be reveresed by more police work, Rhoads said, because many such killings are the result of domestic disputes. Burglaries had especially increased in apartment areas, where access is often gained through balcony doors, he said.

Rhoads noted that some persons may be eligible for low-cost, $10,000 theft insurance offered by private insurers and the U.S. Department of Housing and Urban Development. In order to qualify, he said, homeowners must take certain security measures. County police are available to make free security surveys of homes to determine if they qualify for coverage, he said.

At the press conference, Rhoads named Pfc. Douglas Henegar police officer for the month of December 1977. He was cited for his off-duty rescue of a man from a car that had overturned in four feet of water Dec. 21 in Beltsville. Two years ago, Henegar was saved from possible death by a bullet proof vest when he was shot by a motorist during a traffic stop.