The Reagan administration, while trying to trim the cost of the Medicare bureaucracy, is letting millions of dollars in overpayments and questionable benefits slip undetected through a shrinking staff, a top federal official has complained in an internal memorandum.

Tera S. Younger, director of Medicare's Bureau of Program Operations, said administrative cutbacks have caused substantial drops in the number of Medicare claims investigated and denied as well as in the number of medical providers subjected to audits. As a result, she wrote, the federal health care program for the elderly is paying "drastic increases of as much as 37 percent" in benefits to patients and providers.

The Health and Human Services Department official said figures for the last six months of 1981 show budget cuts beginning to have a severe impact on her department's ability to monitor how the program's $47 billion is spent.

"Benefit payments are increasing, claims investigations and denials are decreasing," Younger said in the six-page memo. "Overpayments are up and service to the beneficiaries and providers is down . . . . Fraud and abuse is likely to increase under reduced monitoring . . . "

An HHS spokesman responded that "we're trying to squeeze the budget" by cutting back on other areas to pay for more audits.

Sen. Max Baucus of Montana, ranking Democrat on the Senate Finance health subcommittee, said, "Medicare officials should spend more, not less, on auditing. While the administration may be able to claim short-term budget savings, in the long run they will lead to more fraud, waste and over-utilization of medical services."

Administrative cutbacks at HHS actually are passed along to the nation's insurance companies, which the government hires to process Medicare claims, decide whether to pay them and mail the checks to patients and providers. Blue Cross and Blue Shield, which handle nearly three-quarters of all Medicare payments, say they have laid off or not replaced about 20 percent of their nationwide auditing staff of 470.

Blue Cross officials say they are now auditing only 37 percent of the Medicare providers, down from 58 percent two years ago. As a result, they say, charges to Medicare from 7,500 hospitals, nursing homes and home health agencies will not be audited this year.

In some cases, Blue Cross reviews of whether Medicare treatment is appropriate have been cut in half. Every $1 spent for these reviews saves as much as $5 by rejecting such claims as those for unnecessary surgery or excessively long hospitalization, Blue Cross officials say.

"We have skilled nursing facilities where we don't even look at the claims any more, we just pay them," said Mary Nell Lehnhard, Blue Cross' Washington representative. "The hospitals know we're not auditing. They're putting in any cost that's questionable, and we're not catching things we used to routinely throw out."

Most of the increased errors, HHS officials say, are in payments for medical services not rendered and in checks mailed to the wrong recipients--the kind of mistakes that could be reduced through better administration.

"The message we are giving the insurance companies is that quality and service are less important than pushing the paper through the system," Younger said in the memo.

Administrative costs amount to only 1 1/2 percent of Medicare's budget. During the Carter administration, Blue Cross officials say, their budget increased by 6 to 7 percent a year. But, they said, they received less than a 1 percent increase this year, to $711 million, and are lagging behind both inflation and a 10 percent rise in the number of claims. For fiscal 1983, HHS is proposing a cutback to $704 million, even though claims are expected to keep rising.

Blue Cross says it is forced to save money by delaying the processing of Medicare claims, cutting back on telephone complaint services and increasing the response time for patient inquiries from 10 to 45 days.