The United States' decision to form a Rapid Deployment Force to cover the Persian Gulf would leave gaps in European defenses if war broke out in both places, the Congressional Budget Office said yesterday in a report on the policy implications of the formation of an RDF.

Since the RDF is made up of existing forces that traditionally have been designated for European combat, their commitment to Southwest Asia would mean fewer forces available for the defense of Europe, the report said.

John D. Mayer Jr., author of the 60-page paper, said this could weaken the balance between NATO and Warsaw Pact forces by as much as 12 percent by the end of the second month of a conventional war in Europe.

In arriving at that estimate, he assumed that the RDF would be a force of 440,000 men, about twice its current strength. Once the RDF was committed in the Persian Gulf, he said, the United States for the first 60 days of a European war could do no more than rush six divisions to Europe.

If the RDF were kept at its current size, and thus draw fewer forces away from NAT0 if war broke out in the Persian Gulf, there would be 20 percent fewer forces available to fight in Europe. This would diminish the NATO-Warsaw Pact balance "by as much as 6 percent," according to the CBO.

The Reagan administration, like the Carter administration, has warned that NATO partners must provide more of their defense in Europe because of the competing demands for U.S. forces in Southwest Asia.

"Such responses on the part of our European allies have not been forthcoming, perhaps because of economic constraints," the CBO report noted.

"Four more fully supported Army divisions, at a cumulative five-year cost of approximately $37.8 billion, would be needed to allow the United States to maintain NATO's stance in the current force balance while simultaneously deploying" an RDF of 440,000 men, the report said.

The current RDF would have little chance of stopping a major Soviet thrust into Iran, the report said, but "could probably serve successfully in support of friendly Arab states involved in regional conflicts, which are not unlikely."

"Hostilities between Oman and the Peoples Democratic Republic of Yemen, or betwen Ethiopia and Somalia, could certainly erupt again in the future and, in fact, would be much more likely than any overt Soviet move into the region," the CBO said in its report entitled, "Rapid Deployment Forces: Policy and Budgetary Implications."