Corinne Sugihara, 24, wanted to be a doctor. So she joined the Navy.

The Navy, like the Army and Air Force, is having difficulty getting and keeping doctors and will pay for Sugihara's tuition, books and fees and pay her $400 a month for living expenses. In return, she agreed to spend at least four years in the Navy as a physician.

Catch 22: When she agreed to serve in the Navy, Sugihara also incurred a bill of $12,000 to $15,000 that she will have to pay during the next four years to the federal government for taxes due on the scholarship given her by the federal government.

What concerns the Pentagon is that Sugihara's tax problem may undermine the principal solution the Pentagon has seized upon to solve its own problem - the shortage of military physicians.

The three branches of the military - the Marine Corps uses Navy physicians - now have about 1,000 fewer physicians than the 11,700 the Defense Department calculates are needed to serve military personnel and their families, according to Col. John E. Murphy, director of planning and policy analysis for the assistant Secretary of Defense for health affairs.

"If we can't provide the care inhouse, we have to buy it," Murphy said in an interview, "If we have to buy it, it's more expensive."

Until four years ago, when more military doctors were needed, more wer drafted. The draft was ended in 1973, and the military switched from the stick to the carrot to attract physicians. Those already serving were given a pay increase and medical school students were offered full tuition scholarships in exchange for four years of service.

Initially, the military scholarship program was assumed to be tax free. Sometime in 1974, however, according to Murphy, budget officials in the Department of the Army asked the Army's general counsel for an opinion on the monthly stipend paid to scholarship recipients for living expenses.

By the time the matter had run its course through the bureaucracy, the Army and the other service branches had been told by the Internal Revenue Service Commissioner Donald C. Alexander wrote the Army's general counsel that a scholarship is not taxable when given on a "no strings" basis, "with no requirement of any substantial quid pro quo from the recipients."

Since medical students receiving Armed Forces Health Professions scholarships agree to serve in one of the armed services, Alexander wrote, their scholarships do not qualify for tax exemption.

In the face of that ruling, Congress enacted a moratorium in 1975. The Tax Reform Act of 1976 reauthorized the moratorium until Dec. 31 of that year, but Congress failed to make the exemption permanent. Anyone entering the program for the first time after Dec. 31, 1976, including Sugihara and about 1,000 other medical school students, now is liable for taxes on both the stipend and the scholarship.

Sugihara's first-year expenses include $9,000 for tuition, $2,100 for an efficiency apartment and at least another $1,000 for food, transportation clothing, books and incidentals. Her income will just about equal and may slightly exceed her expenses, including tuition, except for the matter of paying a federal tax bill in excess of $3,000 the first year.

"There are other scholarships available and those people aren't being taxed on those," Sugihara said in an interview. "The IRS is calling this an income to pay tuition, but it's an income I never get to see and I'm not getting an income to pay this income tax. By imposing a tax on the scholarship, they're defeating the purpose of the program, which is to provide physicians for the armed forces and for underserved areas."

Also affected by the IRS ruling are medical school students with scholarships offered by the Public Health Service. Those students agree to serve in the National Health Service Corps, one year for each year that the tuition is paid, with at least a two-year minimum commitment. The students are obligated to serve in areas designated as having a physician shortage.

According to Dr. Robert Shannon, medical officer for the National Health Service Corps., the program had fewer applicants this year than the previous year for the first time. Shannon attributed the decline, among other things, to the taxability of the scholarship.

Murphy's assistant, Lt. Eleanor S. Matheson, said the military scholarship programs also are picking up indications that in future years the Defense Department may have trouble filling the program with medical school students.

The reason for apprehension is not difficult to understand. As Sugihara said, "I'm already owing service, and I feel that I shouldn't have to owe anybody financially." She will either have to borrow money or ask her parents to help her pay the taxes on her scholarship.

The problem is especially difficult for students at George Washington and Georgetown medical schools, which have the highest tuition rates - $9,000 and $12,500, respectively - for freshmen midical students at any private medical schools in the country.

The Defense Department has several proposed solutions. One alternative, which contradicts the stated policy of the Carter Administration and stands little chance of being adopted, is granting a permanent tax exemption for the scholarships.

An official of the Office of Management and Budget who is familiar with the administration's position said:

"It would not seem to be good policy to tax individuals or parents who work to finance their education or their children's education while exempting from taxation individuals whose educational expenses are paid for by the government."

So the Pentagon has proposed another solution - increase the amount of the stipend sufficiently to allow about 80 per cent of medical students on military scholarships to be able to pay the taxes out of their stipends.

The notion of the government taking more money out of one pocket to put it in another may strike some as unusual, but it would not conflict directly with Carter administration policy and might cost less than granting an exemption.

No increase in the scholarship has been approved. The nearest thing to help being on the way is an amendement offered by Sen. Robert J. Dore (R-Kan.) and already approved by the Senate Finance Committee, to extend the tax exemption another two years. Dole's amendment has not passed the House or Senate.

The Pentagon is concerned but confident. "We will get well," Murphy said. "We assume we will fix the scholarship program. If we don't, we won't make it."