Confirmation hearings on President Carter's nominee to head the Federal Reserve Board have dragged on for more than four weeks with no discernible effort on the part of the White House to speed up a vote.

When Carter nominated industrialist G. William Miller to head the nation's central bank last December, there was no indication that the Senate Banking Committee would fail to send the nomination to the floor by Feb. 1, when current Chairman Arthur Burn's term was supposed to end.

But the day before Miller's routine Jan. 24 confirmation hearing, the Central Intelligence Agency told the banking committee staff that the Bell Helicopter division of Textron Corp., of which Miller is chairman, made a questionable $2.9 million payment in 1973 to a firm secretly controlled by the head of the Iranian Air Force.

Iran bought $500 million of helicopters from Bell in 1973.

The banking committee staff investigated the payment for several weeks. While it failed to turn up evidence suggesting that Miller knew that the late General Mohammad Khatami was a part owner of the firm Bell used as a sales representative, the committee decided that enough of a cloud existed to warrant recalling Miller for questioning next Tuesday.

Yesterday, banking committee sources said the committee poenaed records from Textron's auditor, Arthur Young Co., that are thought to show several Textron divisions engaged in kickbacks, although Bell Helicopter apparently is not one of the divisions in question.

"If the committee decides to call Arthur Young officials, it could go on another two weeks," said one disgruntled Miller backer.

While the White House clearly wants Miller to be cleared as soon as possible - Chairman Burns is edgy as well - it has not pushed committee members to force a vote. All the Democrats on the committee, with the exception of Chairman William Proxmire (D-Wis) appear disposed to vote for Miller, as do most Republicans.

"I'm a minority of one on the committee," Proxmire admitted to reporters last Wednesday after a staff report on its investigation. "I may be a minority of one in the Senate."

But proxmire ran the hearing without a single Democratic challenge to the procedure. In fact, leading Democratic members of the committee - such as Alan Cranston of California, Adlai Stevenson III of Illinois or Thomas J. McIntyre of New Hampshire - were either not present or were there for only a few moments.

Republicans such as Harrison Schmitt of New Mexico and Richard Lugar of Indiana have taken the lead in trying to limit Proxmire's probe to Miller's fitness to head the Federal Reserve Board rather than whether Textron Corp. has engaged in questionable overseas payments.

That type of investigations could take four to six months. The Securities and Exchange Commission has launched such a probe of Textron. The SEC investigation will go beyond the $2.9 million payment to Air Taxi Inc. in 1973.

Miller said in his January testimony that the payment was made to cancel the sales representation agreement with Air Taxi to eliminate commissions that the company would have been owed under the terms of the cancelled agreement.

He also said that he had no knowledge that Khatani controlled the firm through a nominee. He told reporters he would be "amazed" if that were true.

The Senate Banking Committee staff has established that Khatani secretly owned one-third of Air Taxi, even though he was supposed to have sold his ownership in 1965 after the Shah of Iran tightened up conflict-of-interest laws.

Bell officials several times that Kha - from 1964 to 1968 - who alleged he was run out of Tehran by Khatami - told the Banking Committee he told Bell officials several times that Khatami was the secret owner of Air Taxi. William French's lawyer, C. Robert Bell, also said he told Bell Helicopter officials several times that Khatami controlled Air Taxi.

Attorney Bell will testify to that effect Monday and the banking committee also will hear from several Textron officials. These officials told committee investigators that they did not know of Khatami's role and maintain that the questionable $2.9 million payment was legitimate and involved no funds to Khatami or others.

As Miller's nomination hearings drone on embarrassingly long, Federal Reserve officials are becoming concerned not about the conduct of monetary policy or the effects of uncertainty on the dollar, but about the Fed's bureaucratic infighting ability withouta permanent chairman.

While Burns postponed an open market committee meeting last Tuesday to next Tuesday in hopes Miller would have been approved, the agency is functioning normally, insiders say.

But the 73-year-old economist has lost his zeal for the head-knocking that characterizes Washington bureaucracy.