Two former top officials of the Roger Williams Medical Center have asked a federal appeals court to overturn their convictions for paying a state senator to advance the hospital’s agenda, saying the trial judge gave jurors incorrect instructions on the law, prejudicing their cases.

Robert A. Urciuoli, the former president and chief executive officer of Roger Williams, was convicted last October of conspiracy and 35 counts of mail fraud for his part in hiring John A. Celona, then a Democratic state senator from North Providence, to advance the hospital’s legislative agenda.

In verdicts reached after seven days of deliberations, the jury also convicted Frances P. Driscoll, a Roger Williams senior vice president, of one count of mail fraud. The appeals court has allowed both defendants to remain free pending the outcome of their appeals, saying there were “substantial questions of law” raised by the instructions that U.S. District Judge Ernest C. Torres gave to the jurors prior to their deliberations.

Urciuoli is facing a three-year prison sentence. Driscoll is facing eight months in prison followed by eight months of home confinement. In their appeals to the 1st U.S. Circuit Court of Appeals in Boston, both are asking that their convictions be voided and that they be granted new trials.

The convictions came as part of a sweeping federal probe, still under way, into State House corruption.

Celona, a former lawn mower repair shop owner who became the chairman of the Senate Corporations Committee — the committee that controlled the fate of health-care legislation — was the government’s star witness at the defendants’ trial. He has pleaded guilty to selling his office to Roger Williams, the CVS drugstore chain and Blue Cross & Blue Shield of Rhode Island, and is serving a 2½-year federal prison term. He faces an additional 18 months in state prison after he finishes serving the federal sentence.

Celona was hired in 1998 as a consultant for an assisted-living facility and nursing home affiliated with Roger Williams. But prosecutors said he was paid by the hospital’s top officers to perform favors for the medical center and promote their political agenda. From the time of his hiring until January 2004, Celona was paid $260,638 for his work for Roger Williams. He resigned from the legislature in March 2004 after the state police raided his house and carted away boxes of records and computer equipment and other senators called on him to quit.

The defense argued that Celona’s hiring by Urciuoli was open and legitimate and that his position was not a “sham” but involved substantial work recruiting residents to The Village at Elmhurst, the assisted-living center that was partly owned by Roger Williams (and which has since been sold and renamed). They noted that it was Celona who sought out the position, claiming he needed extra income.

The appeals of both Urciuoli and Driscoll center around Torres’ instructions on the law. He told the jurors that in deciding to return convictions for honest-services mail fraud, they could consider any work that Celona performed on Roger Williams’ behalf, both work related to his official duties and votes at the State House and anything “under the cloak of his office.”

But the defense lawyers — Martin G. Weinberg and Kimberly Homan of Boston for Urciuoli, and John A. “Terry” MacFadyen for Driscoll — argued that those instructions were overly broad and prejudicial. Torres’ instructions, they argued, allowed the jurors to convict their clients for conduct that is in fact not illegal and for activities “entirely unrelated to the legislative duties which the public elected him to perform.”

Torres, they argue, “erroneously expanded the reach of the federal mail fraud statute in a manner that is both unprecedented and flatly inconsistent with this court’s honest services fraud jurisprudence and with precedents from other Circuits.”

They say that Torres erred by allowing the jury to consider activities that Celona did for the hospital that had nothing to do with his duties at the General Assembly — including lobbying the cities of North Providence and East Providence to increase their ambulance runs to Roger Williams and arranging meetings with executives of Blue Cross & Blue Shield of Rhode Island and UnitedHealthcare — that were entirely unrelated to Celona’s legislative duties.

In his brief, MacFadyen said that in states like Rhode Island, which have part-time “citizen” legislatures, conflicts of interest are both “endemic” and “integral to the legislative process” and that certain conflicts are tolerated under state law and ethics rules.

“Rhode Island has attempted to balance the good and the bad of its chosen system through the creation of an Ethics Code administered by a constitutionally-created Ethics Commission,” MacFadyen wrote. “This code distinguishes conflicts which necessitate recusal by a legislator from those which are deemed tolerable because they do not affect the legislator to any greater degree than they affect the entire body of his/her profession.” The onus is on the legislator to know when he or she must abstain from voting, he said.

MacFadyen said the Roger Williams case “is about the difficulties which may ensue when non-legislators, not covered by the Ethics Code, enter business relations with a politician who is, and when that politician proves to have moral blinders, an oversized ego and feet of clay.”

In analyzing Celona’s activities, MacFadyen noted that Celona “never claimed that Roger Williams required him to vote or act in a particular way as part of his job. Although he testified that he ‘did things for Roger Williams,’ he could not say he sold a specific vote.”

He also pointed out that when Celona was first hired at Roger Williams, he had “so little influence” at the State House “that he could not command an office on the premises.”

tbreton@projo.com