A federal grand jury here is investigating whether the head of a Chicago-based accounting firm gave kickbacks or other financial incentives to D.C. Deputy Mayor Alphonse G. Hill in return for receiving work on city contracts, according to a lawyer for the firm's head and other sources familiar with the inquiry.

The investigation has focused on the relationship between James Hill Jr., the managing partner of Hill, Taylor & Co., which has been involved in several city contracts, and Deputy Mayor Hill, according to Adam Bourgeois, James Hill's attorney, Alphonse Hill and other sources.

Bourgeois said yesterday that U.S. Attorney Joseph E. diGenova's office had informed his client that he was a target of the grand jury's investigation but "he's never done anything improper or illegal" and had "never given Al [Hill] anything at all."

Deputy Mayor Hill said yesterday that he has done nothing wrong and that James Hill's firm has not received any special treatment from the city.

"He [James Hill] has never given me a dime," Alphonse Hill said during an interview in his office. "I don't own anything with him. I have no assets with him, emphatically."

The disclosure of the investigation, in which the FBI is participating, comes a week after former D.C. deputy mayor Ivanhoe Donaldson began serving a seven-year prison sentence for defrauding the city of more than $190,000 and is the latest in series of federal investigations of D.C. government.

Alphonse Hill and James Hill are not related but are longtime friends who were graduate school classmates at the University of Chicago.

In a separate development, Hill and three other District financial officers were sharply criticized by Alvin C. Frost, a senior D.C. cash management analyst, who charged in a Jan. 31 letter to the mayor that the city's senior financial management "is rife with incompetence, mismanagement, negligence, political favoritism, intimidation [and] indifference."

Frost, alleging a number of irregularities in financial services contracts, recommended that Barry initiate a corruption investigation and suspend Hill and three of his aides.

Frost, who criticized senior financial officials last year for a decision to invest $100 million with a New Jersey securities firm that subsequently went bankrupt, noted in the letter that he intends to resign from the city government after April 1 and is considering becoming a candidate for mayor or the D.C. City Council.

Alphonse Hill declined to comment on the specific charges, calling Frost a "nerd and an imbecile."

He said yesterday that the current grand jury investigation is an outgrowth of a D.C. inspector general's review of similar allegations about his relationship with James Hill that were leveled in late 1981 or early 1982 by two persons -- one now employed by the D.C. government and the other a former city worker.

The inspector general's office, then headed by Joyce Blalock, investigated the allegations and by mid-1982 found no evidence of criminal wrongdoing, Alphonse Hill said.

The deputy mayor said he was told by Blalock that he should have put "a little more distance" between himself and James Hill, in view of their longstanding friendship, and that the city's contracting procedures surrounding the work peformed by James Hill's firm were "a little loose."

Alphonse Hill said the U.S. attorney's office subpoenaed some of his financial records in 1982 after, he assumed, Blalock and possibly one of his accusers notified the FBI.

He said that by 1983, when no official action had been taken, he thought the matter had been resolved. But, Hill said, nearly a year ago he was told federal officials had begun subpoenaing his bank records again and were again examining his relationship with James Hill. He said that as recently as last week the grand jury had subpoenaed more of his bank records and his American Express bills.

Hill said that federal prosecutors have not told him that he is under investigation. He said he had had conversations with James Hill in which James Hill had discussed the investigation.

In a telephone interview last night, James Hill called the federal investigation a "fishing expedition."

James Hill said federal officials have never come up with any evidence of wrongdoing. "Just because I know Al Hill, that doesn't mean I did anything wrong," he said.

Sources familiar with the current federal investigation said that the grand jury is looking at several D.C. government contracts that James Hill's firm received either as a primary contractor or a subcontractor to other firms after Alphonse Hill joined the Barry administration as the city's first controller in August 1979.

James Hill said his firm first began doing business with the city in 1981 after opening an office in the District to take advantage of the D.C. government's minority contracting program.

James Hill said he currently has only one direct contract with the District government, for ensuring the integrity of the D.C. lottery's daily televised drawings. A city official familiar with the lottery contract said Alphonse Hill did not play a role in the award of the contract.

James Hill's firm has also been a minority participant in several D.C. contracts awarded to nonminority accounting firms.

For example, James Hill's company receives about $45,000 a year as one of two minority accounting firms assisting Coopers & Lybrand, a national accounting firm, in conducting the annual audit of the city financial operation, according to John Silton, Coopers & Lybrand's managing partner here.

Silton said that Alphonse Hill had nothing to do with the firm's decision to select James Hill's firm.

Barry promoted Hill to deputy mayor for finance in 1983 and placed him in charge of the city's financial operations, including the city's $2 billion-a-year budget and expenditures by city agencies.

Bourgeois said he believes the current investigation stems from "baseless" allegations made to federal authorities by a disgruntled former employe of James Hill's firm.

Alphonse Hill said that the financial records he volunteered in the earlier Blalock investigation of his relationship with James Hill triggered a civil suit filed against him by the U.S. attorney's office in mid-1983. That suit alleged that Alphonse Hill concealed and lied about $50,000 in personal assets he could have used to pay off a defaulted loan he obtained through the U.S. Small Business Administration before he joined the Barry administration.

In December 1983, Alphonse Hill paid the federal government $80,000 to settle the case. Hill did not admit any liability and denied that the government was due any money. Hill said at the time that he settled the case because it would have cost him more money to defend himself in court.