Whose hand will be on the nuclear trigger of the controversial U.S. Pershing II and cruise missiles scheduled to be deployed in West Germany, England and here in Italy beginning in December 1983?

American Army and Air Force personnel will man the missiles in these three countries, but it is not yet settled what veto -- if any -- the host country will have if the moment comes when a U.S. president, after consulting with his NATO allies, releases them to be fired.

The conflicting political needs of the coalition Italian Cabinet, which must be able to assure parliament that any firing will have Italian approval, and of West German Chancellor Helmut Schmidt, who reportedly insists that West Germany will not have control on the weapons, is forcing the Reagan administration to reassess its original plan to have a uniform control system for all of the NATO missile sites.

That plan would put the weapons and their operations under total American control.

For more than 25 years, control over use of American nuclear weapons stationed in Europe has been a sensitive problem, and it promises to be even more so since the new missiles will be able to hit the Soviet Union directly.

NATO officials fear that the touchy, behind-the-scenes political problem over control of the missiles could feed into the broader controversy over whether deployment of the theater nuclear missiles will actually take place.

The Italian government, much to the discomfort of U.S. officials, wants to have an Italian officer physically present at the firing of any of the 112 U.S. cruise missiles scheduled to be based on its territory beginning in the spring of 1984, according to government officials here. This presence will give the Christian Democrats and Socialist politicians who have put the missile decision through parliament a basis for asserting that no missile will be fired without prior Italian approval.

Schmidt, officials in Bonn said, has told U.S. officals that Bonn refuses to have direct control over a nuclear weapon that could strike the Soviet Union directly, and in the case of the Pershing II in a matter of six to eight minutes. While NATO treats these two new missiles as a modernization of existing forces, the Soviets perceive them as a qualitative and threatening change. Schmidt "wants the U.S. and NATO to be fully responsible" for launching any of those German-based weapons, a NATO official said.

No problem of control has developed with the British, who will take 160 cruise missiles because of the special relationship and understandings that have developed between the two countries.

NATO has put in place a highly structured system for requesting and releasing nuclear weapons in the event of a crisis. Final authority over release is highly classified and a matter known only at the highest levels of the government and the country on whose soil the weapons are based. Moreover, the process is sufficiently complex that U.S. Army field manuals build in a 24-hour period between the time a commander wants to use a nuclear warhead and the time he gets an order to do so.

According to NATO's scenario, before any warheads could be released by order of an American president, ambassadors of the North Atlantic Council, NATO's political arm, would gather around a table in Brussels to voice their national views on the recommendation of the Supreme Allied Commander in Europe, who currently is the American Gen. Bernard Rogers. In his other role as commander of all U.S. forces in Europe, the NATO commander also passes his request on to the president in Washington.

During an actual crisis, it is more likely that the discussions would be handled by the leaders of NATO governments on some special communications link.

When other nations, during 1979, were brought into the Pershing-cruise missile program, one Italian official said recently, "We were not given an opportunity to change the control notion."

Now, however, Rome wants to expand its role in the actual firing of the missiles.

Italian sources said the government wants some bilateral agreement between the Italian and U.S. governments that would formally establish a joint control program. And then some physical arrangements must be made at the missile site that would permit an Italian to prevent the U.S. Air Force team from launching any warhead.

The Italians want a so-called "two-key" system similar to one that existed 20 years ago when U.S.-built Jupiter intermediate-range missiles -- which were capable of striking the Soviet Union -- were stationed briefly on Italian soil.

At that time, the U.S. missiles were actually manned by the Italian military and the U.S. forces controlled only the warhead. In order to launch one of those missiles, both the American military man at the site and an Italian officer would have to receive a release order from his own military commander.

Lacking such an order, one or the other officers could insert a key and prevent the launch.

Under newer control systems, the "two-key" approval of both officers would be required before the system could be launched.

What the Italians will get remains to be seen. U.S. officials want to delay until closer to the deployment date any discussion of problems such as control over firing. And they most of all want to prevent differences between the allies' approaches from cropping up, fearing that any such instance could be blown up into a major propaganda issue by the Soviets and their communist supporters in Western Europe.