Serious crime reported in Montgomery County rose by 2.4 percent in the first six months of 1987 compared with the same period last year, including a 37.9 percent increase in reports of forcible rapes, according to the police department's quarterly crime report released yesterday.

The department does not see 2.4 percent as a significant increase because the county is growing substantially and an increased crime rate can be expected, according to police spokesman Sgt. Harry Geehreng. The rate "has been going up every year and we feel . . . we've kept it to a moderate increase," he said.

In 1986, serious crime increased 3.9 percent over 1985, and all crimes in 1986 were 12.1 percent higher than in 1976.

"I don't think any of us is happy with an increase," said Sgt. Barney Forsythe of the Rockville Investigative Bureau. " . . . We'd be happy to see decreases across the board."

The increase in forcible rapes reported -- from 58 in the first six months of 1986 to 80 in the same period this year -- was the most significant jump in the six-month statistics, which reflected moderate increases in burglary, larceny and moderate declines in robbery, aggravated assault and car theft.

Police say the increase in rapes may be due in part to more victims reporting the crime.

"I think {the increase} has more to do with reporting than it does with actual rapes," said Detective Philip Raum of the Bethesda station. "A little bit of change in the reporting can make a big difference," he said. The FBI estimates that only one out of 10 sexual assaults is reported, and Raum said that if for some reason two out of 10 victims report them, there is suddenly a 100 percent increase in reported rapes.

Police this month charged a Baltimore courier, Tony M. Chatman, with four rapes and an attempted rape and are investigating his role in several other rapes. Chatman alone would account for about one-quarter of the increase, Raum said.

The report said police made 38 arrests in rape cases this year compared with 32 in the same period last year, an 18.8 percent increase.