The Carter administration last week opened itself to a new-and potentially serious-question: Do the president and his top economic policymakers actually have their act together as the administration has been claiming since last November's dramatic dollar-rescue effort?

The question arises as a result of the administration's extraordinary display over the past two weeks in connection with a Treasury-backed campaign to prod the Federal Reserve Board into raising interest rates as a device to help slow the overheating economy.

In a mind-boggling round of maneuvers, Carter abruptly pulled the rug from under his top economic advisers, badly undercut his own secretary of the Treasury as head of the administration's economic team and summarily barred any high-level review of the proposals-all virtually in full public view.

Almost as stunning were appearances of serious chinks in the relationship between the president's policymaking team and the Carter-appointed chairman of the Federal Reserve Board, G. William Miller-whom White House advisers cite as the man who prompted the president to act in the first place.

Until last week, outsiders presumed that the two sides were working in tandem-through weekly luncheon meetings between Miller and Treasury Secretary W. Michael Blumenthal, who led the administration's campaign for higher interest rates. Carter's political lieutenants were taking a back seat.

But last week's saga provided some hints that the earlier Treasury-Fed accord had become mired in a series of memoranda, notes, end-run attempts and pressure tactics not generally seen here since the Johnson administration was openly warring with then-Fed chairman William McC. Martin.

In short, the nation's economic policymaking apparatus was back in disarray.

The spectacle began benignly enough about a month ago, when Blumenthal and some key aides began worrying that the industrial sector of the economy might be overheating-a concern that now is shared by many non-government economists as well.

The fear was that the unexpected boom was causing excess demand and exacerbating inflationary pressures. The administration's new wage-price guidelines, designed to work only in a period of relative slack, were being strained to the breaking point.Prices were going through the roof.

Worried that continuation of the boom might "rachet up" the rate of inflation-and possibly result in a deeper slump later this year-Blumenthal began pushing to tighten present policy. The budget was too hard to change and too slow in taking effect. Interest rates seemed the quickest course.

At first, other Carter advisers were reluctant, fearing that a sharp rise in interest rates would bring on a deeper downturn. But when new figures showed continued high inflation and overheating, the economic policy team began to panic. Ultimately, only Labor Secretary Ray Marshall demurred.

When top Carter economist Charles L. Schultze ultimately acquiesced, it was viewed a major turning point by key administration advisers-marking a belief that the overheating was so potentially dangerous that policymakers now were willing to risk a recession in order to dampen the current excess demand.

Although an interest rate rise might not bite hard immediately, Blumenthal argued it would "send a signal" to big businesses that were borrowing heavily to finance excessive inventory buildups. Reportedly, he urged a rise of half a percentage point, the minimum amount that analysts said would have any effect.

After stories leaked out about the economic advisers' consensus, Blumenthal decided to float the idea more publicly. In a speech prepared for delivery in Dallas, the Treasury Secretary referred openly to the possibility that the administration may have to "risk" recession to slow inflation.

But the speech, while widely distributed here, never was delivered as written.At the last minute, Blumenthal deleted the key paragraphs, without notifying reporters back in Washington. The pronouncements made the headlines anyway, but Blumenthal technically was off the hook.

The policy recommendations, however, apparently never made it to Carter for a normal review-or even to the traditional channels of the administration's Economic Policy Group, the cabinet-level policymaking group that provides background and formal recommendations on economic proposals.

Instead, without any further consultations, Carter sent terse notes to Blumenthal and Schultze ordering them to drop the subject entirely. According to key White House political lieutenants, the president also groused pointedly that his advisers too often had been wrong about the economy's resiliency.

The White House side of the story was that Carter had reacted to a complaint from Miller, who supposedly called the president directly to complain that the pressure was interfering with the Fed's traditional independence. Fed sources, however, insist Miller made no such call.

At a press conference a few days earlier, Carter confidently predicted that inflation soon would slow and the economy would emerge in good shape - publicly disputing warnings by his advisers that the new round of overheating was threatening to keep the price spiral alive.

That Friday morning, an obviously muzzled Blumenthal appeared at a meeting with reporters where he was suspiciously reluctant even to discuss the notion of raising interest rates. "I never have publicly called for an increase in interest rates," he asserted. "I think present policy is right on track."

Blumenthal's argument was that the overheating was serious, and is not ebbing rapidly enough. His fear was that unless some action were taken soon, inflation would worsen and inventory-building would accelerate-paving the way for a steeper downturn.

Miller took the opposite tack. To him, the economy was showing signs of slowing down a bit, and to boost interest rates now would risk pushing the economy into a recession. Both fiscal and monetary policy already had turned restrictive. If a recession did come, Miller didn't want the Fed to be blamed.

By the end of last week, it was clear that Miller had prevailed. After a meeting of the Federal Open Market Committee, the Fed's chief policysetting panel, the markets showed no signs of upward pressure on interest rates. If the Fed has decided to tighten further, the signs are yet to come.

But to many observers, the decision by the Fed and others is second to the jolt to the administration's policymaking image, particularly in the wake of last November's dollar-rescue effort, when concerted action by the White House fostered new confidence that the Carter team had come of age.

Where previously there had been carping among the president's economic and policial advisers, in November the administration was united-and willing to take risks. Where Carter earlier had been wishy-washy on inflation, in November he seemed finally serious.Out of chaos, order had come.

But the new series of incidents shattered that post-November image and revived gnawing doubts about the administration's policymaking performance-and about Carter himself. There were these considerations:

Whether Carter decided correctly or not in burying the Blumenthal campaign for higher interest rates, there is widespread agreement among critics that he did so for the wrong reasons-ostensibly in reaction to a procedural scrap rather than on the basis of any formal policy review.

As a result, one of the most important questions of the time-whether the overheating is so bad that it's worth risking a deeper recession to help cool the economy down-will not even get a full-fledged hearing. Aides say that so far as the president is concerned, the issue is dead.

If the current economic team is so smooth-working, why did the principals allow themselves to get into the position of seeming to claw at each other that way? Couldn't this have been settled at one of the group's frequent luncheon meetings? That's the way it's worked in previous administrations.

Why wasn't the administration's proposal for boosting interest rates backed up with a full range of staff analysis, as such proposals are supposed to be? (By contrast, the Fed had its homework done with a full-fledged staff study. Miller later brushed off the Treasury predictions as a "hunch.")

The maneuvering also left the administration open to renewed charges of indulging in "stop-go" economic policies, constantly changing at the first sign of shifting conditions without waiting to allow its previous measures really to take hold. (The November action was to have stabilized policy some.)

And what about the president himself? If Carter really has his economic act together, why didn't he call team in and talk over the problem? Why all the sniping at his top advisers? If Carter doesn't like them, why doesn't he fire them? And why isn't the overheating issue getting an airing?

At week's end, Blumenthal was on vacation, none of Carter's other top economic advisers were talking about the incident and initial indications in the money markets were that the Fed has decided for moment not to alter its previous policy course.

As for the economy, doubts remain on both sides. Although the latest figures on the gross national product show that the economy's growth slowed markedly in the first quarter of this year, the statistics included only January and February numbers, which were depressed by adverse weather.

Meanwhile, fresher statistics on durable goods orders, employment levels and other indicators show that the overheating issue is far from settled. And even miller warned that the Fed still may tighten monetary policy if the growth rate balloons again in the current quarter.

By week's end, there was little real doubt that the administration would be facing tough decisions in the months ahead. But as one high official observed last week, the question once again was not so much on substance as on procedure. It was: Is this any way to run a railroad?-again? CAPTION: Illustration, no caption; Picture 1, 2, and 3, President Carter badly undercut Treasury Secretary Blumenthal (right) as head of the economic team, and serious chinks appeared between Carter's policymaking team and Federal Reserve Chairman G. William Miller. By Bill Perkins-The Washington Post