Faced by a threatened $28 million shortfall in District of Columbia tax revenues, the Barry administration has ordered department heads to prepare for cutbacks that could freeze hiring and promotion of city employes during the next nine months.

In a sternly worded directive released yesterday at the District Building, City Administrator Elijah B. Rogers gave officials until Monday to choose ways to cut spending for the rest of the fiscal year.

Each agency was given a target figure for the amount to be slashed. These included 8.3 million from the public schools, 4 million from the Police Department, 1.5 million from the Fire Department and 1.5 million from the Corrections Department.

While most agencies probably can meet their goals by freezing all but mandatory hiring and by curtailing purchases, Rogers said that "for other agencies it may be necessary to initiate reduction-in-force actions."

Although the city's operating budget tops $1.5 billion this year, officials said it is so precariously balanced that any cuts would have to come from reductions in programs or personnel.

"Increases in income are not likely," Rogers bluntly told the department heads. "In fact, this situation arises because of the need to make downward adjustments in our projected revenue collections."

Issuance of the directive does not automatically mean that the cuts will be imposed, Rogers told reporters. It represents "a contingency plan" that would be invoked if the revenue predictions come true, he said.

The biggest downward revision, Rogers said, resulted from a court decision last September that will reduce commercial real estate tax collections by $20 million during this fiscal year.

Superior Court Judge Paul F. McArle struck down a law passed by the City Council that would have required commercial property owners with tax bills of $100,000 or more to pay the full annual amount in one lump sum instead of two installments.

Thus the city will lose a one-time windfall it would have gotten before the end of the fiscal year, Rogers said. While the second installment will be collected in March 1981, it will be too late to pay obligations that fall due this fiscal year.

By law, the city cannot run a deficit, although it routinely over the years has held back on paying bills that arrive toward the end of a fiscal year. In 1978, it carried over $1.15 million in such debts and paid them in the new fiscal year.

Rogers said the city ended the 1979 fiscal year in the black. An audit report is due later this month.

Other causes of the revenue short-fall, Rogers said, included less income than expected from the city's civilian parking enforcement program and a decision by Congress to estimate revenues $3 million higher than the city's projection.