Angry members of a key House subcommittee held up a District government request yesterday to transfer $4 million in unspent police department funds to the city's prison system, scolding officials for ignoring a congressional mandate to use the money to hire more police officers.

"This problem started out as a mild irritant. It has now reached a crisis point," said Rep. Julian Dixon (D-Calif.), chairman of the House Appropriations subcommittee for the District of Columbia and in the past an advocate of greater home rule the city. "My personal conservation is that there has been some foot-dragging on this."

City budget and personnel officers appearing before the subcommittee to give the official reason for the no hire policy said a reassessment of the police entrance examination as possibly discriminatory against blacks has temporarily halted recruitment. Funds earmarked in the city budget for additional officers thus should be transferred to pay corrections department bills, they said.

But City Administrator Elijah Rogers said later in the day at the District Building that "our position is that we do not need them [additional officers.]"

The subcommittee's criticism came in a rare hearing on an otherwise routine and common request bg the District to transfer funds from one agency to another. Normally, such fund transfers are automatically approved, with no hearing being called.

But yesterday, the committee refused to approved the transfer, taking it "under submission" for a decision within the next several days. Dixon said his current inclination was to vote to allow the transfer, but he said he doubted that he could convince a single colleague on the subcommittee to go along with him.

At issue is a congressional mandate, issued last December, directing the city to raise the number of police officers to 3,880. Congress earmarked $6 million in the budget for the fiscal year that ends Sept. 30 to pay about 260 additional officers.

But the city has beefed up the force according to the directive. Current strength of the department, Police Chief Maurice T. Turner told the subcommittee yesterday, is 3,619 officers. Twelve more are now being hired, but beyond that, there are no firm plans to hire more police, he said.

"They have just totally ignored the committee and the mandate," Said Rep. William H. Natcher (D-Ky.), who initiated the congressional call for more police on the city's streets. "I think the mayor is just as wrong as he could be."

City Budget Director Gladys W. Mack and Personnel Director Jose Gutierrez said recruitment has virtually ceased since the police entrance examination administered last March is suspected of being biased against blacks.

But in drawing up his budget for the 1982 fiscal year beginning Oct. 1, Barry requested only enough money to pay 3,621 officers -- a fact taken by the subcommittee members as evidence that the city does not intend to hire the extra officers, examination or not.

"I know obstructionism when I see it," Rep. John E. Porter (R-Ill.) told the city officials. "Your job was to get the officers hired."

At a press conference yesterday, Barry continued to cite problems with the examination as the hold-up. Although he declined to attack the subcommittee head-on, he did say that he had the City Council should be the ones to decide how many officers to hire.

Dixon said the battle threatens to alienate members of the powerful subcommittee who have traditionally been friends of the District. The panel has approval power over the District's budget, and without such approval the city cannot spend any funds, even its own tax revenues.

The police exam given by last March 28 was one developed by the federal Office of Personnel Management and currently in use by the U.S. Park Police and the uniformed branch of the Secret Service. The same exam has been used by the city in the past.

But Gutierrez said that the results showed that 61 percent of whites passed the exam, while only 40 percent of blacks passed -- an unacceptable discrepancy. He said he anticipated a court challenge if the city tried to hire officers based on the raw results of the exam, and added that within 45 days he would propose to Barry alternatives for skewing the results of the test to arrive at a better ratio of blacks to whites.

If all else fails, Guitierrez said, the city will have to develop an entirely new exam -- a process that could take months.

Police Chief Turner said he opposed the effort to take the $4 million from the police department budget, explaining that he could use it to pay officers overtime.

Budget director Mack said the money needs to be shifted primarily so that the corrections department can meet its payments to the Federal Bureau of Prisons for housing District inmates.

Also yesterday, Mayor Barry signed a new three-year contract with the police department's rank-and-file officers. The contact, the first reached under the city's new personnel system, provides a $1,000 bonus for each officer in the first year, a $1,000 increase in base salary and a $400 bonus in the second year and a general pay increase of 7 to 9 percent in the third year. In addition, the contract calls for the city to increase health benefits.