A Chicago-based firm handled millions of dollars in District employes' salary funds for months without a contract to perform the service, signing a formal pact with the city two days after questions were raised by The Washington Post.

The firm involved is Group Insurance Administration, headed by Robert H. Carter III, who was recently summoned before a federal grand jury here that is investigating contracts issued to the firm by former D.C. deputy mayor Alphonse G. Hill.

The Post requested copies of the city's contracts with GIA on Feb. 25. Two days later, Hill wrote a contract for the employe deduction service, although GIA had been performing the work since December 1985, city officials said yesterday.

City Administrator Thomas Downs said he recently canceled the contract because of a regulation instituted Feb. 26 requiring such contracts to also be approved by the Department of Administrative Services, which was not done in this case.

The work done by GIA involved parceling out to individual firms about $6 million a month in payroll deductions for such items as car loans and insurance premiums. Downs said that work is now being done by city employes.

District Controller N. Anthony Calhoun said yesterday that as he understood the situation, the reason there was no contract with GIA was that the work was considered a "different kind of animal because it did not involve District funds."

Instead, the individual companies receiving payroll deductions paid the city 6 cents and GIA 44 cents per deduction, he said. Because the fees were considered city employes' money, rather than District funds, "this wasn't the typical procurement," he said.

Calhoun said the city heard no complaints about the work, adding that GIA had posted a $1 million performance bond. In January, the city signed another contract with GIA to process employe optical and dental benefits.

GIA, which Carter says is the only minority-run health claims processor in the country, has held three contracts with the District. The largest is the optical and dental contract, for which only minority firms were eligible. City officials have refused to release copies of the contracts.

A spokeswoman for Carter, reached at an office he maintains in New Orleans, said he would have no comment on his contracts with the District.

Alphonse Hill resigned as deputy mayor last month after he disclosed that he had received $3,000 in cash from James Hill, president of a Chicago auditing firm that does business with the District government. A lawyer for James Hill has said the payment was a "courtesy" for Alphonse Hill's having helped arrange a private business deal between James Hill and Carter.

Alphonse Hill's role in the award of city contracts to James Hill's firm is a focus of the federal investigation.

The D.C. Lottery Board recently canceled the bids it received for a contract to monitor the televised lottery games. The contract is currently held by James Hill's firm, and a city contract committee had recommended that the firm win the renewal bid. Controller Calhoun said the contract needs to be rebid because of premature disclosure that Hill's firm was the favored bidder.

Hill's firm also assists the auditing firm of Coopers & Lybrand in performing the city's annual audit. Hill & Taylor is one of two minority firms that provide the required 35 percent minority participation in the four-year contract, which began in 1984. An official with Coopers & Lybrand said he is "unsure" whether Hill & Taylor will continue in the contract.

James Hill could not be reached. His attorney, Adam Bourgeois, said neither he nor his client would comment.