A D.C. City Council committee voted yesterday to launch an investigation of hiring, leasing and contracting procedures in several city agencies - including the Department of Human Resources - but left undecided how much money should be spent on the probe.

Despite objection by some Council members that the anticipated $700,000 price tag was too high, the government operations committee adopted without opposition a resolution by Council member Arrington Dixon (D-four) to authorize the investigation.

The committee's approval was an unexpected victory for Dixon, who earlier this week had appeared to be losing support among several key Council members who had apparently grown cold to the idea of a large-scale Council probe.

The crucial test for the proposed investigation will come next week before the Councils committee of the whole, when the Council will begin deciding how much money to spend and how much authority the investigators will be given.

Ever since Dixon announced Jan. 11 that a full-scale investigation could cost as much as $750,000, several Council members have asserted that such a price was too high for a budget-pinched city government.

Some Council members who previously advocated a thorough Council probe have backed down in the face of preliminary reports from three other investigations of alleged nepotism and cronyism in DHR. Those reports have disclosed a chatoic personnel operation in the agency, but found little hard evidence to support individual allegations of favored treatment.

At yesterday's meeting, Dixon attempt to thwart opposition based on the high cost of the probe by proposing that the money come not from the Council's own $2.3 million budget, but from a $16 million budget already authorized by Congress for a special commission on city financial management.

In September, 1976, Congress established an eight-member Temporary Commission on Financial Oversight of the District of Columbia to help set up a better bookkeeping system for the city, whose books were found to be too confusing to be property audited.

Dixon argued yesterday that even if the Council's probe did not help establish such a system, it would help overhaul the city's personnel system - on which two of every three city dollars is spent - and the city's contracting and leasing system, which make up "a significant portion" of other city expenditures.

Council member Marion Barry (D-at large), said he believed that the money might not be obtainable from the commission and could take too long to get. Barry argued instead that the scope of the probe be scaled down and that more emphasis be placed on immediate legislation that could remedy personnel system ills that already have been disclosed.

The committee's recommendation to the full Council will be to seek the money from the commission. But it will be the committee of the whole, which has jurisdiction over Council budget matters, that will make the decision or how much money to spend on the probe and from where the funds should come.

As outlined by Dixon, the investigation would use a staff of 21 persons and take nine months to carry out. A second committee recommendation approved yesterday, however, would provide that the staffing pattern outlined in the resolution could be altered.

Voting in favor of the resolution along with Dixon and Barry was Douglas E. Moore (D-at large). The only other committee member present, William Spaulding (D-five) remained quiet during the voice vote, refusing to vote either yes, no or say that he abstained.

The Council's investigation is one of six probes - including one by the U.S. Attorney's Office here - that have begun since mid-November into alleged irregularities in DHR.