D.C. Police Chief Burtell Jefferson has sent a confidential memorandum to city officials saying their proposed budget cut for his department "will raise serious questions" about the police force's ability to combat increased crime in the city.

The internal memorandum to assistant city administrator Gladys W. Mack also said the proposed $3 million cut would have to be absorbed by the loss through attrition of 138 uniformed officers. The cut would effectively freeze the hiring of new employes.

"I would be remiss for failing to point out that the alarming increase in crime . . . has grave potential impact on the quality of life for the the entire community," Jefferson said.

Major crime -- homicide, rape, robbery, for example -- increased 10 percent in the District of Columbia during 1979, according to preliminary crime statistics.

Jefferson said he had taken steps to improve the quality of service delivered by setting goals to meet these austere times. However, the reductions that are being mandated raise serious quesions about this department's ability to met this threat.

Even with the major improvements in the management of this organization," Jefferson said, "the basic tool that I have at my disposal is manpower to meet this challenge, vis-a-vis high visibility crime patrol, directed at specific crime hazards.

"There is no question that this community will experience some degradation in service, i.e., response time on calls for service, traffic enforcement and preventive patrol."

The police chief was responding to a directive from City Administrator Elijah Rogers, who last week ordered department heads to find ways to cut spending to absorb a $28 million shortage in the city's budget.

Rogers said yesterday he had received Jefferson's memorandum and that "the chief has said that, if he has to absorb the cuts, this is what he would do. Whether or not we agree with the chief will have to be decided."

Rogers said that Mack will review the chif's proposed cuts and make recommendations to him. "It may change altogether," he said.

Mack said yesterday she expects to make recommendations to Rogers in the next few days.

In his memo, Jefferson said vacancies in admistrative staff will not be filled and major reductions in staff position have already occurred.

About 68.8 percent of the department's manpower is in the field operations division, which includes uniformed officers and homicide detectives, among others. There are 4,001 members of the police force, although the department has an authorized strength of 4,120.

If the department is forced to absorb the budget cuts, the force would be under 4,000 much lower than the high of 5,100 authorized in 1971.

In his memo, Jefferson also requested that $3.5 million that Congress cut out of the department's budget request last year for retirement benefits be restored. He also requested $3 million to cover a 7 percent pay raise for those in the pension program.

Since the oil crisis, the cost of gasoline for the department's fleet of cars has increased to the degree that he asked that an original request of $500,000 be increased to $629,400.

"I must again emphasize that the overtime costs ($658,400) associated with the pope's visit and Iranian student's demonstration must be recovered from the federal government if our expenses are not to exceed our fund availability," Jefferson said. "This obviously is also true of costs associated with any additional demonstrations."

A spokesman for Sen. Partick J. Leahy (D-Vt.), chairman of the D.C. appropriations subcommittee, said he didn't know if the city would be reimbursed for the overtime costs with the pope's visit and the Iranian student demonstrations.

The D.C. school board last week told the Barry administration that the board will not seek ways to cut the current school budget by nearly $8.4 million as it had been asked to do to help meet the budget shortage.

School officials said the cuts threatened textbooks and equipment purchases, court-mandated tuition grants for special education and the maintenance of buildings at projected levels.