An extraordinary split has developed between military and civilian intelligence agencies over conclusions reached by the director of the Central Intelligence Agency about the balance of strategic military power between the United States and the Soviet Union.

The military agencies are arguing that the CIA summary of a top-secret government-wide assessment of the power balance, which goes to President Carter, is "not representative" of the analytical work that went into preparing that assessment.

Perhaps more importantly, the military contends that the job of comparing the U.S. and Soviet forces and how they might fare in an atomic struggle constitutes what is called a "net assessment." Preparing such assessments, they contend, is the prerogative of the Joint Chiefs of Staff and the Defense Department rather than the CIA.

The CIA, this argument goes, should confine itself to figuring out what the Soviets are doing.

The dispute centers on the latest version of the National Intelligence Estimate, which goes from the nation's top intelligence officer. CIA chief Stansfield Turner, a former admiral, to the president.

That Turner is at the center of this dispute is not surprising. The ex-Navy man has been the target of some criticism from both military and civilian defense officials in recent years as he, under Carter's orders, has solidified his sometimes controversial control over the nation's intelligence apparatus.

Because the National Intelligence Estimates are widely circulated among the top rungs of government, and are so authoritative, these estimates have great importance within the bureaucracy in shaping future U.S. national security policy on many issues.

Officials say that the NIE summary contains what is called a "footnote" but which in fact is a sharp dissent by the Pentagon's military-run Defense Intelligence Agency (DIA) together with the intelligence chiefs of the three-armed services.

Administration sources call the breadth of the split with the civilian-run CIA "unprecedented." A well-informed Pentagon source says: "It is fair to say this is probably as strong an assertion of dissent on the part of the DIA to the director of central intelligence" as has been registered.

The States Department's Bureau of Intelligence and Research and the super-secret National Security Agency did not join in the dissent, sources say.

The actual conclusions of the report are highly classified, but sources suggest they contain a mixed bag of assessments that trouble the military.

On the one hand, the defense agencies are said to believe that the report underestimates the relative momentum of the Soviet strategic military buildup in comparison to that of United States, arguing in effect that the picture is even grimmer than presented.

Yet the military also contends other sources say, that the new report overestimates the Soviet threat that could be mounted against the Pentagon's planned MX super-missile.

The military is counting on the MX as its future land-based, long-range missile force. Critics contend the Soviets, with their bigger missiles, will always be able to lob enough atomic warheads at the MX shelters to make survival of a few of them not worth the huge cost, estimated by some at more than $60 billion. Supporters of MX argue that the Russians wouldn't use their missiles in that fashion.

CIA officials say that full-scale net assessments, involving such things as paper war games to figure out who wins, are indeed the Pentagon's job. The CIA claims it is not doing that but rather has been using "a more sophisticated form of analysis in recent years" and "adding some judgments" to its findings rather than just counting Soviet missiles.

The CIA officials contend that many people within the government find this technique helpful in assessing the power balance, a claim confirmed in interviews with civilian officials elsewhere in government.

Some CIA officials suspect the military objections at this time may have an element of politics to them, seeking perhaps to take advantage of an election year to support those arguing for higher defense spending in face of the Soviet threat.

Pentagon sources suggest it undoubtedly will be left to the president to resolve the dispute over who does what kind of assessment. The report summary also has gone to Capitol Hill, and sources say the House subcommittee of intelligence oversight probably will begin closed-door hearings next week on the report, including the disputed "footnote."

The National Intelligence Estimates, produced by the entire U.S. intelligence community, normally include at least two main volumes, the summary and the back-up factual and analytical data.

The summary section of the disputed NIE, number 1138, was completed in mid-March. The second volume of back-up data is scheduled to be circulated very soon, sources indicate.

In the past, there have been other dissenting footnotes to these reports. But officials suggest they usually have been over technical matters, such as the debate over the range of the new Russian Backfire bomber and whether it is aimed at U.S. targets or other targets closer to the Soviet Union in China.

In the current dispute, the DIA and military chiefs are understood to have "disassociated" themselves from the summary presented by Turner, contending that it concentrates too much on quantitative information and gives too little weight to Soviet military doctrine, policy, overall capability, momentum and future programs.

Similarly, the military is said to contend that the kind of analysis used in the summary distorts judgments and that these are shaped too much by U.S. thinking, rather than on Soviet thinking, on strategic matters.

Though Turner also is not without his critics elsewhere in the civilian-run agencies of government, on this issue the former admiral seems to have supporters.

One administration source says he has "a grudging admiration for Turner in refusing to budge from his position once he and his analysis are convinced they are right."

Another suggested that Turner was refusing to allow the NIEs "to become sterile documents" and refusing to "let the MX go by without focusing a light on it."