The D.C. City Council's plans for an ambitious and expensive investigation of leasing, contracting and personnel practices in city government appeared to be severely crippled yesterday before the probe could even get going.

Council member Arrington Dixon's resolution asking for $700,000 to finance a nine-month investigation under the direction of a $39,000-a-year chief counsel was immediately criticized by some of Dixon's colleagues as too expensive for a budget-pinched city government.

Other Council members, including some who serve on Dixon's government operations committee, objected to not being consulted by Dixon before the resolution asking authorization of the probe was drawn up.

By the time the bill was referred to committee after 30 minutes of often stormy debate, it appeared clear that Dixon (D-four) would have a difficult time getting enough votes to pass the package and might have to cut down its scope considerably to gain Council approval.

Council member John A. Wilson (D-two) was among four members who said the proposed price tag was too high."I don't know where Mr. Dixon's going to get the money unless he's going to steal it from someone," Wilson said. "I think we could all save him a lot of trouble by saying up front that we're not going to go for that."

William Spaulding (D-five), a member of the government operations committee, suggested that the resolution was motivated by "arbitrary and self-serving ends" and disowned any sponsorship of it. "This is not a product of the committee. It is a product of the chairman of the committee," Spaulding said.

Dixon responded by accusing several Council members - including Chairman Sterling Tucker - of turning a sudden cold shoulder towards the plans "after a number of months of posturing and tribal dancing" in favor of a prompt and thorough investigation.

"It seems to me," Dixon retorted, "that the very folk who have been pressing for expeditions proceedings are now extending the process even more."

Plans for a Council investigation were first announced in early September, following accusations in the news media of widespread mismanagement and questionable hiring, leasing and contracting practices in the D.C. Department of Human Resources.

Ever since their inception, the Council's investigation plans have been embroiled in internal controversy and, in the view of some Council members, embarrassingly slow moving.

On Dec. 12, nearly a month after the first published allegations, Chairman Tucker announced that the Council's long-anticipated probe of DHR would not take shape until two to four weeks later, after the Council received reports from other investigations then in progress.

Two days later, Dixon contradicted the chairman, saying the investigation would begin the following week and would utilize expert lawyers and researches from outside city government - "national level prosecutors and investigators of the Watergate committee type."

Dixon assmbled a five-member blue ribbon advisory panel, including two former Watergate investigators, who submitted their recommendations on how such an investigation should be carried out.

It was largely on the basis of these recommendations that the resolution presented yesterday by Dixon asked the authority to assemble a staff of at least 21 persons to carry out the task.

Tucker referred the resolution to Dixon's committee for consideration, but also said it would have to be reviewed by the committee of the whole, which includes all 13 Council members and is chaired by Tucker.

The joint referral, Dixon complained afterwards, would probably slow down the resolution. Dixon plans to consider the resolution at next Wednesday's government operations committee meeting. It could be at least three weeks before a final vote on the investigation authoriation is taken by the Council.

The apparent tug-of-war over the investigation was motivated by several factors according to District Building sources, including a genuine concern with its possible costs and political maneuvering among some prominent Council members.

Since the allegations first were reported Nov. 18, four other city probes of DHR have begun, along with a federal investigation of suspended DHR director Joseph P. Yeldell and a preliminary inquiry by the D.C. Board of Elections and Ethics into the financing of Mayor Walter E. Washington's 1974 election campaign.

The three other city agencies involved in the investigations are all being significantly affected by the amount of time and resources being spent on the probes.

The elections and ethics board has asked the mayor and Council for additional money to hire three more staff persons and has delayed some of its investigations because of a shortage of investigators.

The mayor's Office of Municipal Audit and Inspection has at times used up to one-third of its 30-person staff on its investigations of DHR niring, leasing and contracting practices. "It has placed some strain on our ability to get all of our other work done." David Legge, the office's director, said yesterday.

D.C. Auditor Matthew Watson, whose overdue report on DHR personnel practices is to be presented this week, has used his entire even-man staff almost exclusively on the investigation for most of the past seven weeks.

The requests for additional manpower come at a time when many other city departments - including DHR - are clamoring for more workers and closing some vital services because they lack people to run the services. "How are we going to justify an investigation of this scope?" one Council member said privately. "Hell, the chief counsel would be making as much money as Joe Yeldell."