D.C. City Council member John A. Wilson (D-Ward 2) has asked the D.C. auditor to conduct "an immediate and expedited investigation" into the city's contract with the Pitts Motor Hotel, a shelter for homeless families.

"Simple logic dictates that it should not be costing the city well over $2,000 per month and well over $30,000 per year per family to provide room and board in the less-than-luxurious Pitts Motor Hotel," Wilson said in his request to D.C. auditor Otis H. Troupe.

Hotel owner Cornelius C. Pitts said he was unaware of Wilson's request. "It's utterly ridiculous," said Pitts, when he told of the audit. He said 52 families were staying at the hotel at 1451 Belmont St NW.

"I'm not afraid of an audit," said Pitts, who said he had had a contract with the city to shelter the homeless since 1968. "When the government was trying to find a hotel that would take these families, no other hotels would take them."

The Pitts, Wilson noted in his letter, had received $1.5 million of a $1.7 million contract with the city as of April 30. The hotel was spotlighted as a welfare hotel with "Ritz prices" this week in a two-part news report by television station WDVM (Channel 9). According to the reports, Pitts receives $84,000 a year in salary and earned more than a half million dollars in profit last year. Pitts refused to comment on the figures.

"When I saw the TV report I was incensed . . . ," said Wilson. "I didn't have the slightest idea we were spending that amount of money or that we weren't getting a dollar of service for a dollar spent. If the TV report is correct, the city is being stuck up -- or the city is sticking up the taxpayers."

The hotel receives the largest single share of the $5.8 million the city's Department of Human Services spends to house the homeless, and it was cited in a congressional hearing on the plight of the homeless in March as one of the most expensive hotels for the homeless in the nation.

The city pays Pitts $42.85 a day for a family of four for a room, which totals $1,285 a month plus $12.48 per person each day for three meals a day, which totals $1,497 a month for a family of four, according to the city's social services commissioner Audrey Rowe. The monthly bill: $2,782 for a family of four.

Members of a House subcomittee holding hearings yesterday on the Human Services budget for fiscal 1987 questioned the Pitts' price.

Rowe said the average stay at the Pitts is 149 days, "far in excess of what we would want." Some families, she said, stay as long as 220 days. She also said that the city's funds for emergency housing are being taxed because U.S. marshals "are evicting 60 families a day."

"Most of the money spent goes to feed people," said Pitts. "People shouldn't look at the total price the city pays. They should look at the unit price, what I charge for each meal and each day's stay. The total price just points to the need; there are a lot of homeless families in the city."

But Wilson said, "It would be cheaper to rent a facility or buy the Pitts . This is . . . just another example of the mismanagement and possible unethical practices of the Barry administration."