Republican Governor Carcieri lashed back Tuesday at Lt. Gov. Elizabeth Roberts, a Democrat, for what he calls her “irresponsible and erroneous accusations” about his administration’s agreement to pay $370,000 to the Lucas Group for its consulting work on the state’s Medicaid overhaul.

“There is no wrongdoing by anyone in the administration, and to imply such is grossly negligent,” said a statement issued by the governor’s office. And, “there was never a ‘no-bid, no-contract agreement’ with the Lucas Group,” the statement said.

The administration has been unable to produce a bid or contract for the Boston-based company that has emerged as a major player in Carcieri’s securing of a federal waiver giving the state unprecedented freedom in how it spends its Medicaid dollars on health care for the poor, the elderly and the disabled.

In fact, 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 the waiver from the Bush administration. 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 state Senate June 9 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.

Carcieri’s statement outlined this series of events on the payment: “After several months of disagreement with the Lucas Group, a settlement was reached after intensive mediation facilitated by retired Associate Justice and former Attorney General Richard Israel.”

The statement acknowledges: “No formal contract was ever signed and or formal purchase order was ever issued to the Lucas Group for payment ... [however] the Office of the Governor agrees with Justice Israel that the State did benefit, and payment to the Lucas Group is appropriate under the circumstances.”

On Monday, both Roberts and Attorney General Patrick C. Lynch publicly demanded details about the Lucas Group settlement, which came to light Friday, and a key state senator said the situation is “puzzling” enough to merit a Senate inquiry.

Roberts 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.”

A big chunk of the settlement — $150,000 — was paid last week, as required under the pact. Roberts sent the governor a letter Tuesday asking him to withhold any further payments in light of the “numerous questions [that] have arisen about the appropriateness of the relationship between” the Lucas Group and the Department of Human Services.

In an accompanying statement, she said: “State money cannot be spent without responsibly following purchasing and procurement laws and regulations. … I call on Secretary Alexander to provide a detailed timeline of the events he set in motion surrounding the engagement of the Lucas Group and bring transparency to any negotiations with the Lucas Group before and after the apparent dispute over payment.”

kgregg@projo.com