Country music singer Tommy Beckham, alias Eggleston Zimmerman, was feeling chipper as he returned to his Alabama jail cell last July.

A man of many credentials, from self-described Central Intelligence Agency operative to "bishop" of a variety of obscure sects, Beckham had just been acquitted of federal fraud charges stemming from his promotion of a country music concert that was never held.

Undeterred by all this, investigators from the House Assassinations Committee interviewed him the next day in a sweltering cell at the Mobile, Ala., city jail about the murder of President Kennedy. Beckham, 35, reportedly poured forth claims of having known Lee Harvey Oswald in New Orleans and assertions that Kennedy was the victim of a conspiracy and that he, Thomas E. Beckham, knew who had taken part in it.

"To tell you the truth, most people don't believe him," Beckham's own lawyer. Jeff Stein of Mobile, says succinetly. A one time fugitive from New Orleans District Attorney Jim Garrison's fruitless investigation into the Kennedy murder, Beckham finally returned to tell an Orleans Parish grand jury in 1968 that he really knew nothing about the President assassination in 1963.

The House investigators, however, apparently took Beckham quite seriously. "They wanted names, dates, places," Stein recalled in a telephone interview.

It was a small, but illustrative slice of the approximately $1.5 million that the controversial House investigation has thus far cost. Operating in nearly total secrecy since the accession of G. Robert Blakey as chief counsel last June, the House Assassinations Committee has built up a sprawling staff of 109 individuals and hired more than 30 consultants whose names the committee refuses to disclose.

Under the terms of a perhaps unprecedented "Non-Disclosure Agreement" obtained by The Washington Post, the consultants cannot, without written permission, even "indicate, divulage or acknowledge" that they work for the committee until it goes out of business. At least one member of a group of 14 pathologists who attended a secret committee seminar in September to review JFK autopsy records says he interpreted the intimidating strictures as a warning that they could go to jail if they even discussed the metting. Yet by all available accounts, the seminar produced nothing startling.

"Doesn't this give you a sense of deia vu" demands assassination expert Harold Weisberg who has been highly critical of the House investigation. "They're doing the same thing the Warren Commission did. It's worse than that now because they have the experience of the Warren Commission behind them. You've got to have this stuff subject to another point of view. The press has to be able to air it."

Committee members plainly disagree. Chairman Louis Stokes (D-Ohio) says he feels the panel's "gag rule" against any discussion of the investigation has served it well. Rep. Richardson Preyer (D-N. C.), chairman of the subcommittee investigating the JFK murder, said "the fact that it [the investigation] has been out of the headlines in the last few months has helped change the mood of the House."

"We were embarrassing the House every day a few months ago." Preyer said, recalling the controvery between the first chief counsel, former Philadelphia prosecutor Richard A. Sprague, and former committee Chairman Henry B. Gonzatez (D-Tex). "Now that's over."

Appointed June 19 as Sprague's successor, Blakey, a former Senate staffer and Cornell University law professor, has taken firm charge to the committee staff. Committee members such as Rep. Harold S. Sawyer (R-Mich.), maintain that Blakey has improved morale tremendously and put the inquiry on a thoroughly professional track.

But some former staffers and others privy to various aspects of the committee's work disagree. They describe Blakey as a professonal martinet who insists on strict discipline from his investigators while letting the investigation itself run off in a dozen different directions at once.

The behavioral discipline is indisputably strict.In the view of some it is also childish and demeaning. They point, for example to an Aug, 1 memo to the committee staff from Blakey, listing "some Dos' and Don'ts' that should be followed in the conduct of our investigation, especially when on trips."

Among the rules:

"Do not conduct interviews in your hotel room with a member of the opposite sex."

"Do be cautious in fraternizing with local residents."

"Do not have meals in locations that are noted for their drinks and not their cuisine."

"Do avoid excessive alcoholic drinking when on assignment whether on or off duty."

"Do in dealing with any person you come in contact, be courteous, considerate and patient, even in th face of extreme provocation."

Do not discuss or get involved in political or controversial topics with anyone."

"Do after working hours know the general whereabouts of the other members of the team."

"Do not visit establishments that have or appear to have questionable reputations unless on official business."

Underpinning all this is the four-page Non-Disclosure Agreement, initiated after Blakey took charge and required of all staff members as well as consultants "as conditions precedent for employment or engagement or my continued employment or engagement with the Select Committee, the United States House of Representatives or the United States Congress." In other words, says one lawyer acquainted with the terms of the document, those who sign it are presumable ruling themselves out of a job anywhere else on Capitol Hill if they break part of the agreement.

It has 16 sections, including one that demands immediate reporting to the committee of any effort by outsiders such as reporters to obtain information. In addition to acknowledging the possibility of criminal prosecution for leaking proscribed information. the signers also agree to be liable for $5,000 in civil penalties "as a reasonable estimate for damages to the credibility and effectiveness of this investigation."

Information that may not be disclosed "by words conduct or other-wise", at least during the lifetime of the committee, covers any cata received by the select committee, presumably including even matters of public record. Some material, such as "any information pertaining to intelligence sources or methods as designated by the director of central intelligence," may "never" be disclosed without special permission. Committee Chairman Stokes must also "consult" the CIA director before clearing for publication any article written by a staffer or consultant which "may include" proscribed information.

"What kind of an independent investigation can you have with provisions like that?" demanded one former staffer who declined to be identified. "This is theoretical world they're setting up, not a practical world for investigating murder."

The chief counsel, who likes to be called "Professor Blakey," declines to comment on any phase of the investigation, reciting a committee rule declaring that the staff shall not discuss "the substance or procedure of their work" unless authorized by Stokes. Preyer or Del, Walter E. Fauntroy (D-D.C.), chairman of the subcommittee investigating the assassination of the Rev. Martin Luther King Jr. in 1968.

Asked, for instance, why the committee would be interviewing someone like Thomas Beckham when it has yet to decide who killed the President in Dallas' Dealey Plaza on Nov. 22, 1963. Blakey said simpy "substance and procedure." He made the same respouse we asked to list in a general way what he regarded as the inquiry's accomplishments thus far.

It seems plain, however, that the two-pronged investigation into the Kennedy and King murders is pursuing an elusive and expensive skein of rumors and allegations of conspiracy before having satisfied itself - from the ballistics, medical photographic, eyewitness and other evidence - about who the murderers were. The committee appears to be looking for helpers before having settled on the principals, who may or may not have had any helpers.

The panels travel summaries show that it has been busy pursuing not only Beckham and other aspects of the zany Gatrison investigation, but also seoterica such as the "Milteer connection." Now dead, Milteer was a right-wing organizer for the States Rights Party who happened to have been taped - two weeks before Kenndy was killed - about how the President might be shot with a high-powered rifle on a forthcoming trip to Miami.

"Where's the relevance?" demands Weisberg, who uncovered much of the material on Milteer years ago. "That's okay for a writer, but not for a congressional committee investigating a crime. How many people theatened to kill Kennedy? To kill King? They're beyond counting. Could all of them have committed the crime? They've got to establish relevance first. They've got to begin with what really happened."

More recently, investigator for the House committee journeyed to New York to interview Marita Lorenz, a self-proclaimed Mata Hari, who asserted that Watergate buglar Frank Sturgis, an old friend of hers, drove with her and several others, including Lee Harvey Oswald to Dallas several days before the assassination. Then, last week. Sturgis was arrested on charges by Lorenz that he tried to intimidate her from testifying before the House committee.

The charges were dropped Friday in Manhattan Criminal Court when a review of seven taped telephone conversations between Lorenz and Sturgis showed all were amicable. "A lack of any substantiation of her charges impairs her credibility," the court was told of the putative congressional witness.

As for Beckham his lawyer said House investigators had hoped to see him again after his client stood trial on still more fraud charges in Arkansas, allegedly for posing as a naturopathic physician. But the charges were dropped.

"He [Beckham] was supposed to meet one of them the House investigators in Mississippi, but he never showed up," Stein said. "They've contacted me a couple of times to see if I've heard from him, but I haven't"

Even though no public hearings are in sight, the committee which expects its current $2.5 miilion budget to last until about next Mareh, evidently foresees no trouble in getting a new appropriation next year. One committee meember said wryly that they will probably be able to get more money be simply $99[WORD ILLEGIBLE] out that they haven't embarrassed the House for months.

Asked if that approach would work an [WORD ILLEGIBLE] to House Speaker Thomas P. Tipt O'Neil Jr. (D-Mass) replied lightly "why not?"