Just two months after taking office, D.C. police chief Burtell M. Jefferson got caught this week in the crossfire of an old dispute over the size of the police force. The dispute pits the City Council, which wants to reduce the force, against Rep.William H.Natcher, (D-Ky.) who wields considerable influence over the District budget.

Jefferson testified at a council hearing in favor of a $2.4 million outlay to maintain a police force of 4,141. The outlay, an increase in the city's budget for fiscal 1979, which begins next Oct.1, was officially requested by Mayor Walter E. Washington.

The mayor acted under terms of a congressional resolution that is providing funds for running the city during the 1978 fiscal year.

At the insistence of Natcher, chairman of the house D.C. Appropriations Subcommittee and an outspoken advocate of a large police force, the resolution provides funds for maintaining a 4,141-member department.

Despite limited home rule, Congress still reviews and enacts all city budgets. That puts Natcher in the position of being able virtually to dictate some city policies.

Because retirements and resignations have reduced the police department by 54 persons, Jefferson recently took the first steps to recruit new officers to fill those vacancies.

Jefferson was in the witness chair for less than a minute before council member David A.Clarke (D-Ward 1) voiced displeasure at the situation.

Speaking softly to the new chief, Clarke said the mayor had undercut the council's decision last year to reduce the police force by 264 during the 1979 fiscal year. If the council prevails, Clarke said, the police department would have to fire the 54 new officers.

Deputy D.C. budget director Gladys Mack, moving into a vacant chair alongside Jefferson, said the mayor "would not make a decision" that would run contrary to the views of Congress.

Clarke called that "presumptuous," but absolved Jefferson of blame. The mayor, Clarke told the chief, "is your boss." But he suggested that the chief confer with the council over such matters.

Council chairman Sterling Tucker called Clarke's discussion with Jefferson "important, necessary and predictable."

Like Clarke, Tucker said that "consultation may well be necessary so it doesn't place one branch of government against the other."

Whatever action the council takes on the mayor's police request - and a rejection of it seems likely - the stage will be set on Capitol hill for the replay of an encounter last year between Natcher and city officials.

With Washington and Tucker looking on, Natcher asked Jefferson's predecessor as chief, Maurice J. Cullinane, whether he personally supported the city's request to cut the police force. Cullinane said he did not. Jefferson now seems sure to be asked a similar question.

Jefferson's appearance was the high point of the council's all-day hearing on the mayor's request to add $22.6 million to the 1978 city budget and $26.6 million to the 1979 budget.

The biggest single increases in both budgets are being sought by the Department of Human Rssources. An additional $9.4 million is requested for 1978 and $7.8 million for 1979.

Albert Russo, the department's director, said the increases would make possible a 5 percent increase in welfare benefits on July 1 and another 5 percent on April 1, 1979.

For a family of four receiving benefits under the program of assistance for families with dependent children, the current $314 monthly payment would rise by $16 on July 1.

However, Congressional action on the 1978 budgetary proposals is uncertain, since the city is operating on a stopgap funding resolution rather than on a formal budget. That presents a tricky parliamentary situation in getting any increases approved.

At the outset of the hearing, Kenneth Back, the city's director of finance and revenue, presented new and increased forecasts of tax collections.

Because of an improving economy, he said, revenues are expected to increase by $18 million in both 1978 and 1979. The biggest single increase expected this year is $8 million in gross receipts and franchise taxes on banks and public utilities, followed by a $4 million rise in personal income taxes.