For more than two years, the Montgomery County police force has been unable to attract, screen and train enough new recruits to keep its manpower up to its authorized strength of 781 officers.

Because there are now 720 active officers on the force, some rank-and-file officers are complaining that police patrols are spread too thin in some areas of the county and it takes longer than it should to respond when word of a crime reaches headquarters.

High-ranking police officials and county bureaucrats say that the increase in response time has been negligible. They are concerned however, at the persistent problems the force has had getting new officers out on the street.

For instance, in 1978, some 36 officers left the department. But a variety of factors limited the size of the current recruit class-the first such class in two years-to 15.

The county's problem, as police officials tell it, was not in attracting candidates. Two years ago, more than 1,000 people applied for jobs on the county force.

But 200 of these did not have the required 60 college credits. Many of the remaining 800 were screened out by the battery of physical, psychological and intelligence tests. And others, discouraged by the time-consuming applications process, took jobs elsewhere.

Even so, by the time the class was scheduled to begin two months ago, the department had more than enough qualified applicants to fill the 30 available spaces. But only five women and five minority applicants had qualified. Under department policy, one third of all recruit classes must be made up of women and one-third must be minorities.

According to county police spokesman Nancy Moses, during the 13 months of screening, some of the qualified women and minorities among the applicants took other jobs-some with the District police force.

County officials have become increasingly concerned in recent weeks about the combined recruitment and understaffing problems. Last month, County Executive Charles W. Gilchrist announced a new plan to bring as many as 40 new officers to the force by the ed of 1979.

Among other things, Gilchrist announced that the starting salary for a rookie officer has been raised $500 to $13,254, and nine police officers have been detached from all other duties to run a recruitment campaign.

But despite the campaign, the number of vacancies may outstrip the number of new recruits by the end of the year, according to Don Ryan, the department's budget analyst, leaving the department at about 93 percent of capacity.

Officers within the department differ as to how this understaffing affects Montgomery County residents. "No one has really come up with a cut and dried rule as to how many police officers you need," said Col. Donald Brooks. "A lot of it depends on the quality of service.

"I'm not saying we can't operate with the vacancies we have," Brooks said. "Because we do operate with them. But we can provide a better service, a greater service at full strength."

Brooks said that the shortage hampered investigations, especially of traffic accidents. Echoing his patrol officers, he pointed out that it is most critical "when you have the very large events, like the montgomery County Fair and the tremendous traffic problems that creates."

But Police Chief Bernard D. Crooke said through a spokesman that he did not feel the understaffing, and the budget cut, was a cause for great alarm.

Indeed the effects of the understaffing are difficult to gauge objectively, because the statistics are ambiguous. For example, the average time it takes to respond to a call has risen about 40 seconds in two years, but police say this could be attributed to other factors, such as the population growth in the more rural northern areas of the county.

For the year 1978, the first year of chronic understaffing, major crime climbed more than 4 percent from the year before; lesser offenses increased by almost 9 percent, according to Col. Wayne Brown. However, Brown cautioned that many factors, entirely apart from the understaffing problem, may have contributed to the increase.

What is not ambiguous is the reaction in the police stations, particularly the Rockville district, with 300 square miles and the fastest growing population in the county.

"We're all shorthanded, very shorthanded," said Capt. John Shaw, commander of the Rockville district. "It's extremely bad on us, and it's become progressively worse. We can't prevent crime by partol. We just respond to calls for assistance. And we have to strip the whole district to take care of one rowdy party of 300 teen-agers."