Questions about Deputy Mayor Alphonse G. Hill's integrity were first raised in 1982 during an investigation by the city's inspector general of Hill's relationship with the Hill, Taylor & Co. accounting firm.

Joyce Blalock, then the inspector general, said recently her investigation was prompted when a city finance employe complained of the success the Chicago-based accounting firm had enjoyed in obtaining city auditing contracts shortly after opening a branch office here in 1981.

Blalock, who also looked into a separate allegation that Alphonse Hill took a cash payoff from a graphics firm, found no evidence of criminal wrongdoing. But she urged him to put more distance between himself and James Hill Jr., the head of Hill, Taylor and a longtime friend of the deputy mayor.

During the course of her investigation, Blalock also discovered that Alphonse Hill had substantial assets in 1977 when he defaulted on a $123,000 U.S. Small Business Administration loan and asserted in a written statement to the SBA that he had no means of paying off the loan.

Blalock's findings led to Hill paying the federal government $80,000 in December 1983 to settle a suit filed against him earlier that year by the U.S. attorney's office here to recover the loan proceeds. Hill did not admit any liability and said he decided it was cheaper to settle the suit than to fight it in court.

In an interview yesterday, Blalock said that when she completed her 1982 investigation she recommended that Hill, then the city's controller, be removed from office. She said she regarded her findings about the SBA loan and Alphonse Hill's relationship with James Hill "as a serious matter about the integrity of a person in a position of great trust."

However, Blalock said, she cannot criticize Mayor Marion Barry and top city officials for retaining Hill because he was being widely praised by private financial experts and others.

"I think there were grounds for Hill's removal ," Blalock said, "but you have to realize everyone else was saying how extremely important Al was."

In January 1983, Hill was appointed deputy mayor for finance at the start of Barry's second term.

Blalock, who left the city government last year to become inspector general for the U.S. Government Printing Office, also played a crucial role in uncovering allegations that led to the corruption conviction last December of former deputy mayor Ivanhoe Donaldson.

Questions about Alphonse Hill's relationship with James Hill were resurrected last year when FBI agents working on an unrelated probe turned up new allegations -- this time after agents learned that James Hill's firm had received a city lottery auditing contract without submitting a formal proposal for it. In June 1985, the U.S. attorney's office began to subpoena Alphonse Hill's bank and credit records and a federal grand jury began investigating whether James Hill had given the deputy mayor any kickbacks or financial considerations.

Alphonse Hill has strenuously denied any wrongdoing. James Hill, who met Alphonse Hill while they attended graduate school at the University of Chicago and later shared an apartment with him in 1967, has termed the inquiry a "fishing expedition."

The deputy mayor has said that he recommended James Hill's firm, among others, for city auditing contracts largely because one of Alphonse Hill's chief financial advisers, Michael Smith, joined James Hill's firm. Alphonse Hill said he introduced Smith to James Hill.

Last year, the deputy mayor, while sitting on a federal review panel, recommended James Hill's firm for a $300,000 federally funded contract to audit St. Elizabeths Hospital. Alphonse Hill said that the firm was the best qualified and that the contract was not being paid for by the city.

Earlier this month, another Chicago businessman, Robert H. Carter III, disclosed that the grand jury had subpoenaed him to answer questions about several hundred thousand dollars in health insurance and disability benefits contracts two of his firms have received from agencies under the deputy mayor's control.

When James Hill's attorney, Adam Bourgeois, disclosed his client's $3,000 payment to the deputy mayor, he said it was not a kickback but was done as a "matter of courtesy" for noncity business Alphonse Hill referred to James Hill's firm. A source familiar with the investigation has said the business was with Group Insurance Administration, a firm headed by Carter