The president of a Chicago firm that handles payroll deductions for D.C. government employes has been ordered to answer questions about the contract before a federal grand jury here next week.

"I just received a summons to discuss my contracts relative to the District, to appear before a federal grand jury," Robert H. Carter III, president of Group Insurance Administration, said in an interview yesterday.

Carter's firm was awarded the contract in late 1984, according to Alvin Frost, a senior cash management analyst for the District on administrative leave, who has criticized the city's financial management practices. Frost recalled that the contract was not bid on competitively, but top city officials who administer the contract could not be reached yesterday to confirm this.

The grand jury is also investigating whether James Hill, the head of another Chicago-based firm, gave kickbacks or other financial incentives to D.C. Deputy Mayor Alphonse G. Hill in return for receiving work on city auditing contracts, according to a lawyer for James Hill and other sources familiar with the investigation.

Interviews with former employes and associates show that Carter and James Hill were business associates.

James Hill's attorney, Adam Bourgeois, said his client and Carter began sharing the rent a year ago on a two-bedroom apartment at 1200 N St. NW, which the two Chicago men used when in Washington on business. Hill has served as Carter's accountant, according to a former executive of the firm, and the two men's offices also are in the same building in downtown Washington.

U.S. Attorney Joseph diGenova said yesterday that he would have no comment on Carter's summons to appear before the grand jury.

However, the summons appears to widen the scope of the federal investigation into possible corruption in the awarding of D.C. contracts dealing with cash management and auditing.

Carter declined to detail what city contracts his firm holds, but Charles E. Davis, D.C. director of pay and retirement, confirmed that Carter's firm has a contract to deduct "allotments," or fixed payments such as monthly insurance premiums and child support, from the weekly paychecks of city employes.

Another firm had been handling the deductions, according to Frost, but D.C. employes were informed that the city intended to discontinue the service by the end of 1984.

However, there was an abrupt change in policy, according to Frost, and Group Insurance Administration was selected by the city to continue providing the service.

"There was no documentation on the contract," said Frost, who recently was reassigned by his superiors after complaining about the city's financial practices. "People were on leave for Christmas and when they came back, it was done."

Davis said D.C. Controller N. Anthony Calhoun awarded the contract. Neither Calhoun nor Alphonse Hill, who is deputy mayor for finance and oversees the city's budgetary and financial management operations, could be reached for comment yesterday.

Under the contract, employes from Group Insurance Administration pick up a magnetic tape of the city's payroll each week and mail it to Chicago, according to Fred Marshall, a former vice president of the firm, who left the firm in early 1985. The tape is mailed because the computer in the firm's Washington office is unable to process it, he said.

The deductions are made in Chicago and the payroll information is transmitted via telephone lines to the firm's District office, which prints the city payroll checks, he said.

Although other details of the contract, including its total value, were not immediately available, the firm that previously held the contract was paid a certain amount per check and had access to the deduction money for a short period of time, according to a source.

Marshall previously worked as a consultant in Alphonse Hill's finance department under a six-month contract from January to June 1984. He said he began working for Carter in June 1984 after he struck up a conversation with Carter at hotel near the District Building. Marshall said he had nothing to do with Carter's contract with the city and left Carter's employ after eight months because Carter stopped paying him.

Marshall said he used James Hill's D.C. office temporarily while he was setting up Carter's office.

According to Bourgeois, James Hill was unaware until recently that Carter had any contracts with the D.C. government.