Nothing bothers a budget officer more than an unexpected bill. A big one was dropped on Valerie Holt on Nov. 9.

That was the day District Mayor Anthony A. Williams (D) announced he was awarding one-time, $1,700 bonuses to 6,500 unionized city employees. The checks would be cut by Dec. 15, Williams promised the unions. The cost: $9 million to $10 million.

An hour before Williams's news conference that morning to announce the bonuses, Holt, the District's chief financial officer, said the mayor had not told her how he intended to pay for the bonuses. Not wanting to spoil the mayor's agreement with labor, Holt held back any criticism. But it was clear that she wasn't pleased.

"We have to balance the fiscal 2000 budget while implementing a tax cut," she said of the pressure to keep the city's budget from running a deficit. "Now, we're looking at the impact of this labor agreement."

With the mayor's office still grasping for a way to pay for Williams's promise, the bonuses have exposed tension between Holt and Williams, who before being elected mayor last year held the job now occupied by Holt.

Williams and Holt maintain that they're getting along fine, but Holt aides say she is frustrated that the mayor's office has not kept her staff informed about the financing of the bonus plan. D.C. officials said yesterday that they are still trying to determine whether Williams's initial plan to pay for the bonuses--by using part of an $18 million severance fund--is allowed under the District's budget bill for next year.

Meanwhile, Holt said yesterday that she has a backup financing plan for the bonuses, which are key to the D.C. government's relations with its unionized work force. But she would not elaborate.

Both Williams's and Holt's staffs agree that tension between the two has risen recently, though neither would discuss that yesterday. The bonus program isn't the first issue over which the two staffs have clashed. In September, Holt was forced to dump a friend whom she had brought in to improve the financial management of the District's Year 2000 computer repair program after the mayor complained about the official's ability.

Holt is an independent city officer who was appointed by the mayor and the D.C. financial control board. It is her job to prepare the city budget and monitor expenditures, including labor agreements. But she was not part of the agreement signed between Williams's administration and the unions Nov. 4.

Besides the bonuses, the agreement calls for the unions to work with Williams in moving city workers to a performance-based system for pay raises and to have some D.C. agencies compete with the private sector for city contracts.

The day the bonuses were announced, Williams was asked how the city would pay for them. He turned to his staff, who said the money would be found in the 1999 and 2000 budgets by switching funds among accounts.

In fact, the bonuses weren't going to be financed that way. That same day, Williams sent a letter to Capitol Hill asking to tap part of an $18 million account intended for severance payments to fired city workers, part of a Williams plan to trim the city work force by 1,000 people. Holt was not told beforehand of the mayor's plans to finance the bonuses from the severance account, a senior aide to her said.

It was too late in the session for Congress to change the budget provision to allow Williams to use the severance fund, though lawmakers did include language in a report accompanying the bill saying that the city intended to spend some of the $18 million on bonuses.

But Rep. Ernest J. Istook (R-Okla.), chairman of the D.C. appropriations subcommittee, said Tuesday that the city would be breaking the law if it did so. He added that Williams had promised him that the fund would be used to reduce the District's work force. "This is not what that money is for," Istook said.

Williams disagrees with that interpretation, and he continued yesterday to try to resolve what his aides characterized as a misunderstanding with Istook.

Meanwhile, the labor unions are anxious because, as their leaders said, many of the 6,500 employees may have made plans to spend the bonus money.

"The mayor wouldn't do anything improper," Williams spokeswoman Peggy Armstrong said yesterday. "We're going to find this money and get it secured."

CAPTION: Chief Financial Officer Valerie Holt says she has a backup plan to fund bonuses for unionized city workers.

CAPTION: Mayor Anthony A. Williams is trying to get congressional approval to tap into a city severance fund.