PROVIDENCE — Support for an investigation of the Carcieri administration’s newly disclosed agreement to pay $370,000 to a no-bid, no-contract Medicaid consultant is growing, with both Lt. Gov. Elizabeth Roberts and Attorney General Patrick C. Lynch demanding answers and a key state senator saying the situation is “puzzling” enough to merit a Senate inquiry.

The administration had insisted for months that John Stephen and the Lucas Group, the Boston company for which he works, had volunteered their time to the state’s effort to win from the Bush administration a waiver giving it unprecedented freedom in how it spends its Medicaid dollars on health care for the poor, the elderly and the disabled.

A partner in the company, Stephen is a former health and human services commissioner in New Hampshire and a failed GOP candidate for Congress. Gary Alexander, who was confirmed by the Senate last Tuesday as Rhode Island’s new secretary of health and human services, campaigned for Stephen and helped raise money for him with a fundraiser at his home.

The first official to speak out publicly since the settlement agreement surfaced last Friday was Roberts, who on Monday said: “I am gravely concerned at the actions of the governor and the Department of Human Services that resulted in a no-bid contract for a personal friend of Secretary Alexander … Circumventing procurement rules, bypassing contract procedures, misleading the public and employing cronyism at any level is unacceptable, and undermines the public’s confidence in government, especially at this crucial time.”

She called on Lynch, a fellow Democrat also eyeing a potential 2010 run for governor, to launch “an immediate investigation to determine if this case constitutes a violation of state laws around purchasing and transparency.”

Lynch needed no prodding.

Within hours, he had sent his own letters to Alexander and Gary Sasse, director of the Department of Administration, seeking both an explanation of what happened and “copies of all documentation related to this settlement and to the underlying claims that formed its basis.”

He also asked them to “kindly identify the source of the funds that will be used to pay for this settlement since, as I understand it, no funds were appropriated in the budget for these services ... nor was the expense incurred through normal purchasing channels.”

The attorney general’s spokesman, Michael J. Healey, said that Lynch “probably like every Rhode Islander ... was shocked by this news.”

“If somebody has failed to follow the DOA’s purchasing rules and regulations in approving this money, there needs to be some accountability, because in the context of our state’s budget struggles, on its face it’s inexplicable,” Healey said.

“Right now we’re not ready to indicate whether or not a full criminal investigation is warranted. We do think, though, that several questions need to be answered,” he said. “First, if the money has already been paid, who paid it: DHS, the Governor’s office or some other agency?

“Second, were the DOA purchasing rules and regulations followed properly? Was whatever agreement that the two sides entered into a binding and valid agreement or was it a handshake deal? ... Last, and on the same theme, we’ve been led to believe that the Lucas Group was providing its services voluntarily. If so, why was the settlement payment approved/made?”

Sen. J. Michael Lenihan, the chairman of the Senate government-oversight committee that spent months probing an earlier no-bid state staffing contract with the Foxboro-based Smart Staffing, said he knows of no law that would allow the Republican Carcieri administration to make a settlement payment to a consultant with no contract with the state.

“It is puzzling to say the least,” said Lenihan, a Democrat from East Greenwich.

He said he has asked his State House legal counsel to “gather as much information as possible,” in anticipation of “likely” hearings, after the legislature adjourns for the year.

When Stephen’s name first surfaced months ago, along with that of The Lucas Group, Carcieri spokeswoman Amy Kempe said the company was working on the state’s global Medicaid waiver negotiations with federal officials on a “voluntary basis.”The waiver is expected to save the state $7 million this year and much more over the next five years by steering the elderly away from nursing homes, redefining who is sick enough to be eligible for certain services and creating treatment networks. Not until last Friday, did the Carcieri administration acknowledge the extent of the company’s role. Asked for comment Monday on Lynch’s letter, Carcieri spokeswoman Kempe said: “We received the letter late this afternoon and are reviewing it. We will respond to the attorney general accordingly.”

kgregg@projo.com