Alexander Grant & Company, the consulting firm that City Administrator Elijah B. Rogers plans to join in late May, has received about $800,000 in contracts from the District of Columbia government within the past year.

The Chicago-based firm, which specializes in accounting and management analysis, was granted two non-competitive contracts in 1982, totaling $740,000, to devise a new system for monitoring the city's capital improvements program.

The firm received two other contracts this year, totaling about $60,000, to help the Department of Human Services audit operations at the Forest Haven facility for the mentally retarded and to assess a new proposal to place a cap on the amount of Medicaid reimbursements that local hospitals may claim from the District.

Rogers and Burt K. Fischer, managing partner of Alexander Grant's Washington office, said yesterday there was no connection between the contract awards and Rogers' job offer as an assistant managing partner.

Both men said that Alphonse G. Hill, deputy mayor for finance and the former D. C. controller, negotiated the contracts with Alexander Grant & Co., and that Rogers did not become directly involved.

"I didn't hire them and I wasn't involved in it," Rogers said. "The only contracts I'm involved in as city administrator involve $5 million or above."

Fischer said that "it was absolutely a coincidence" that his firm received the contract this month to assess the Medicaid cap proposal at the same time he and Rogers were concluding private negotiations.

"My interest in Elijah is what he can do for us in the future, as it would be with any other partner who came aboard," Fischer said.

Rogers, 43, the operational chief of the city government for the past four years, announced last Thursday that he will leave his $67,200-a-year post May 27 to become assistant managing partner of Alexander Grant's Washington office.

Rogers, a former Berkeley, Calif., city manager, said he began preliminary talks with a variety of firms last fall after deciding to leave government, and then stepped up discussions after the November general election. He said he seriously considered accepting an offer from a California firm until recently, but finally decided upon Alexander Grant last week.

"Grant is looking nationally to expand its state and local government business," Rogers said. "I think I can help."

Hill confirmed yesterday that he had prime responsibility for awarding the contracts, but expressed some irritation that Rogers had not advised him at the time that he was talking with Alexander Grant executives about a possible job.

"I'm sensitive to the fact that he Rogers is going there and that they are getting that money," Hill said. "I have to be sensitive in the sense that I don't want people to think we're not doing things in conformance with regulations."

Hill added, "But the decision to grant the contracts was mine and I'll take the heat if it's there."

Hill, a former partner in the Chicago accounting firm of Hill, Whiteside and Wiley, said he has known some Alexander Grant officials for years, including Roger Nauert, a health-care specialist who handled the Medicaid cap contract.

He said he recommended that Alexander Grant receive the $740,000 in contracts to devise a new automated system for monitoring the District's capital construction projects partly because of the firm's expertise in this area.

Hill said he also is concerned that a handful of other firms, particularly American Management Systems Inc. of Arlington, are getting a disproportionate share of the city's contracts. "AMS is a good firm, but they're expensive."

Hill said he did not invite other firms to submit bids before asking Alexander Grant to assess the Medicaid proposal this month because the city was under the gun to decide whether to enter into an agreement with 12 local hospitals to impose a cap--a plan that may save the city $16 million in the current fiscal year.

"We were under time constraints and had to make sure of holding down costs to balance the 1983 budget," Hill said. "So we spent $30,000 on the contract to analyze a plan forecast to save us $16 million. I think it was worth it."