Two crucial questions in the federal grand jury investigation of a $3,000 payment made by a city contractor to D.C. Deputy Mayor Alphonse G. Hill are: When did Hill receive the money and what was it for?

A lawyer for contractor James Hill Jr. said last week the payment was made in 1985 as a "courtesy" to Alphonse Hill for helping arrange a private business deal between James Hill and another businessman, Robert H. Carter III. Alphonse Hill does not dispute this account and moreover filed a statement with the city last week saying that he received the money in 1985.

But this week James Hill's lawyer changed the date of when the payment was made, saying that a review of the records of James Hill's accounting firm, Hill, Taylor & Co., revealed that money actually was paid in two installments, in August and September 1984.

Also, interviews with Chicago businessmen and others active in promoting minority business there show that James Hill and Carter have been acquainted for a number of years, dating to the early 1970s.

Alphonse Hill declined to comment on the apparent discrepancy between his account, contained in an amended financial disclosure report that he filed last week with the D.C. Office of Campaign Finance, and the revised account from James Hill's attorney, Adam Bourgeois. The deputy mayor for finance resigned last week, effective March 31, after the payment became public.

The circumstances of the payment is important because the grand jury is investigating whether Alphonse Hill received kickbacks or other financial considerations from James Hill, whose firm has received hundreds of thousands of dollars in city contracts. Both the deputy mayor and James Hill have strongly denied any wrongdoing and Bourgeois said the $3,000 was not a kickback.

The U.S. attorney's office, in conjunction with the FBI, is examining the circumstances under which the $3,000 payment was given to Alphonse Hill by James Hill, according to sources familiar with the investigation.

If a contractor doing business with the city makes a payment to a city official out of fear that he will lose city business, then the payment could fall under federal extortion laws, according to a federal law enforcement official.

Carter, who runs two Chicago-based insurance companies that have received three D.C. government contracts from agencies under Alphonse Hill's control, said last month that he had been subpoenaed to appear before the grand jury to answer questions about his city contracts. Carter and his attorney have declined further comment.

In an interview this week, James Hill said he knew Carter before Alphonse Hill made the referral, but that "the relationship was casual -- just like you knew somebody casual to speak to them."

Connie Williams, president of the Cosmopolitan Chamber of Commerce in Chicago, said she had known Carter and James Hill since she worked with them on promoting minority businesses in Chicago in the early 1970s.

"Jim [Hill] knew him [Carter] the same time I did," Williams said. She said later that she did not know the nature of the relationship.

James Hill said he did not do any business with Carter until the referral, which he and Bourgeois said was made in 1983, some time before June.

For the last 1 1/2 years, Carter and Hill have shared expenses on a Washington apartment they use while visiting here, according to Bourgeois. A former Carter company executive said recently that for a few months in 1984, Carter's D.C. business operated out of space in James Hill's Washington office.

Alphonse Hill did not report the payment on his original 1985 financial disclosure statement, which he filed on Dec. 30, 1985.

Keith Vance, the director of the office of campaign finance, said he was asked about the disclosure statements when he testified before the grand jury this week.

Vance, who said he had discussed the payment with the deputy mayor, said that based on notes of his conversation with Alphonse Hill, the deputy mayor told him the payment was made "between January and March of 1985."

He said that he now plans to question the deputy mayor further.

After the deputy mayor made the business referral, James Hill began performing audits on a series of insurance contracts Carter had with community action agencies in Michigan, Indiana and Mississippi, according to Bourgeois and officials in those three states.

Carter's most recent D.C. contract, which is for dental and vision insurance for 16,000 city employes and their dependents, was obtained after city officials certified that his firm qualified to participate in the city's special contracting program for minority firms.

To qualify for the program, Carter incorporated a new firm, Group Insurance Administration of the District of Columbia, on June 11, 1984. It was the only one to bid after city officials set aside the contract for minority firms.

William Jameson, the director of the D.C. Minority Business Opportunity Commission, said his agency had had "long discussions" about the firm's eligibility for the city's program because Carter's operations were based in Chicago.

Jameson said that the commission decided to certify Carter's new firm after concluding that it was a genuine D.C. business and receiving written assurances from Carter that Fred Marshall, the employe in charge of the firm's D.C. office, was primarily responsible for running the business here.

Marshall said he was hired by Carter in July 1984 to run the Washington office immediately after working for six months on Alphonse Hill's staff.

Marshall said Carter stopped paying his salary two months after Carter won his minority certification. "I was definitely used by Carter to get that certification . . . to meet certain deadlines," Marshall said. "I was there for the purpose of legitimizing it, as I see now."

After he left Carter's firm and was unemployed for three months, Marshall said Alphonse Hill arranged for him to get a 90-day contract working for City Controller N. Anthony Calhoun, who reports to the deputy mayor.