The District of Columbia government has a sound cash-management system but may be paying too much in service charges to some of the 25 banks that handle city funds, according to a report released yesterday by the U.S. General Accounting Office (GAO).

While generally approving the city's handling and short-term investment of its cash, the GAO urged officials to seek competitive bids from banks in the future before deciding where to deposit funds.

"The wide range in bank service charges indicates that the District may be paying inappropriate prices to some banks," the GAO said.

Many of the current agreements between the city and area banks for depositing city funds were negotiated on a noncompetitive basis, according to the report. Those contracts are due to expire this fall and the city's cash managers have indicated they intend to seek competitive bids for future banking services.

The GAO noted that the District maintained an unusually high average balance at one bank, but recently began to keep a smaller balance there. The name of the bank was not mentioned in the report.

"Less money left in bank accounts allows more money to be invested and thereby increases the District's interest income," the report stated.

City officials were pleased with the GAO's findings, describing the report as the latest evidence that Mayor Marion Barry has brought the city's financial problems under control.

"I've said all along that the District is in good hands," said city administrator Elijah B. Rogers. "Mayor Barry has attracted very competent, talented and experienced public managers who are doing the job that the mayor and the public expect them to do."

Last May, D.C. City Council member Betty Ann Kane (D-At Large) claimed the city was missing out on millions of dollars in potential funds because the Barry administration was handling its cash poorly and wasn't making wise short-term investments. Kane argued that the city could earn at least $50 million a year in interest--more than three times the amount it currently receives--through better investments.

Kane noted that Fairfax County in Virginia, with a $719 million budget, earned about $35 million in interest in fiscal 1981, while the D.C. government, with a budget of $1.9 billion, earned only $16.7 million in interest.

The GAO report did not address Kane's sharp criticism. But in a letter to the GAO accompanying the report, City Controller Alphonse G. Hill said Fairfax County on the average had more than twice as much cash available to invest as did the District last year. On the average, about $103.4 million in city funds were invested daily during fiscal 1981, compared to $263.2 million invested daily by Fairfax County, according to Hill.

Also, the city had a 15.3 percent effective rate of return on its investments, compared to 15.1 percent for Fairfax County, Hill said.

The city invests its idle funds almost exclusively in short-term U.S. government notes.