Serious crime in Maryland decreased for the 15th month in a row, state police announced yesterday, but statistics show that certain violent crimes -- murder and rape -- are increasing in parts of the metropolitan area.

Montgomery County and Prince George's County both reported increases in the number of rapes during the first nine months of this year. Montgomery also reported an increase in murders.

State police officials presented statistics showing an almost 6 percent decrease statewide in violent crime and an overall 10 percent decrease in "serious" crimes.

Serious crimes include breaking and entering and larceny/theft, in addition to the violent crimes of murder, rape, armed robbery and aggravated assault.

State police spokesman Dan McCarthy said that there were 20,319 fewer serious crimes reported in the first nine months of this year in Maryland than during the same period in 1981. But while violent crime overall dropped by 5.8 percent, murders and rapes decreased by only 2 percent.

There were 17 murders in the first 10 months of this year in Montgomery County, according to county officials, compared with 11 in the same period of 1981. Baltimore and Prince George's County, which have the highest rate for rape in the state, did not improve their records. There were 435 rapes in Baltimore City and 309 in Prince George's through September of this year, compared with 418 and 292 respectively for the same period in l981.

Thomas W. Schmidt, Maryland secretary of public safety and corrections, said at a news conference that the decline in crime figures for five quarters in a row "coincides with more stringent sentencing actions taken by the courts, and with the get-tough prison policies . . . in the same time period."

The most dramatic downturn occurred in property crimes: There were 13,347 reported robberies in the state in the first nine months of l981, and 10,774 in l982, a decline of 19 percent.