Nineteen-year-old Wolfgang Melke filled out a form from his local draft board last week and checked off the item that allowed him to refuse to serve in the army on the ground that he was a conscientious objector.

From then on, he was exempt from being drafted. No questions were asked, and he did not have to appear before the draft board or any legal authority to be quizzed about the sincerity of his claim.

Melke's action is being repeated by thousands of young West Germans these days, causing concern in the Bonn government and in the leadership of West Germany's 490,000 member armed forces, the largest European contingent in the North Atlantic Treaty Organization.

Privately, Melke - not his real name - acknowledges that he has thought more about avoiding 15 months of army duty than whether he is really unable to serve in the army as a matter of conscience.

He is, nevertheless, taking advantage of a new law that creates a situation perhaps unique in any major country: the law allows a young man to simply state, without challenge, that he wishes to exercise his rights as a conscientious objector.

The postwar West German constitution has always contained the right to declare such objections. Last year, for example, some 36,000 would-be recruits were awarded conscientious objector status, but all of these men faced some sort of grilling from local authorities to seek evidence of their convictions.

Since the new amendment was passed on Aug. 1, however, 28,000 men have claimed this status in less than four months, a rate three times that of the past. If this rate continues, defense officials say it will drive the army into spiraling manpower shortages beginning next April.

Defense Ministry spokesman Kurt Fischer acknowledges that the upsurge in conscientious objectors has been "a disappointment."

The bill was passed with good intentions. The ruling Social Democratic coalition government, which provided most of the support in Parliament, argued that it was not only demeaning for a young man to have to prove such claims but also difficult for draft boards to sit in judgment upon such moral issues. In some conservative states, others argued, it was hard for a claimant to find a sympathetic ear.

The government hoped, Fischer said, the feeling of responsibility to the state would prevail, tht the concept of a citizens' army would not take advantage of the newly liberalized honor system.

So far, Fischer says, it is clear that many young men "simply prefer to stay home."

Rather than serve in the army, an objector is supposed to serve 18 months in a social service job in a hospital or old-age home. In fact, there are not enough of those jobs to accommodate the huge numbers of objectors.

There are, however, two catches to the present situation. The first is a court challenge.

The new amendment was passed only after two years of debate in Parliament, where it was bitterly opposed by conservative opposition parties who argued that some probing of motives was necessary to prevent the system from being abused.

The conservatives quickly brought a challenge before a constitutional court that is scheduled to begin deliberating the situation Wednesday.

The knowledge that the court would meet late this month may be responsible for the upsurge in conscientious - objector claims that have poured in during the past four months.

A more important catch is in the amendment itself. It allows the defense minister, with approval of the Cabinet, to set aside the amendment if he is convinced the situation will diminish the approved strength of the army.

Social Democratic Defense Minister Georg Leber has already voiced strong reservations and Fisher has indicated that if Leber asks for the amendment to be set side, the approval of the Cabinet is assured.

Almost half of West Germany's 490,000 man force is made up of conscripts. The rest include some 60,000 professional officers and enlisted men plus 200,000 others enlisted under contracts of varying length.

If the present trend continues and the new amendment stays in effect, authorities say it will cut the available pool of some 300,000 draftees annually by about one-third and leave the military potentially short by almost 10,000 men each year.