Serious crime in Montgomery County rose 8.7 percent in the second quarter of this year compared with 1985, while reported rapes rose 55 percent, according to statistics released yesterday by the county police department.

The report said there had been 6,707 offenses in April through June, up from 6,172 for the same three months last year. There were 31 rapes last quarter, compared with 20 a year ago.

Police Chief Bernard D. Crooke Jr. played down the increase in the rape statistics, explaining that the 20 rapes reported during the second quarter last year was the lowest number in the past five years. The high was 49 rapes in the second quarter of 1982, he said. The statistics for the second quarters since then have fluctuated: in 1983, there were 39 rapes; in 1984, 43.

"Of course, one rape is too many," Crooke said, "but the increase of 11 this year over 1985 is within the average."

Crooke said, "There are no trends causing this problem . . . no maniac running around."

Instead, he said, the small number of such crimes as rapes and murders can translate into large percentage increases and decreases. There were three homicides in Montgomery County during the second quarter this year, compared with four a year ago, for instance, resulting in a 25 percent decrease.

Police also recorded increases in auto theft, up 21.4 percent to 572 incidents from 471 last year; larceny, up 10.4 percent to 4,591 from 4,160; residential burglary, up 5 percent to 867 from 826. The categories in which there were decreases included homicides; robbery, down 7.5 percent, to 124 from 134; aggravated assault, down 2.9 percent to 200 from 206; commercial burglary, down 9.7 percent to 280 from 310, and school burglary, down 4.9 percent to 39 from 41.

Sgt. Harry Geehreng, who released the report, said cumulative statistics show that serious crime in Montgomery County is up 7.7 percent for the first six months of this year compared with the same period last year.