Federal prosecutors yesterday told an appeals court that a trial judge gave correct legal instructions to a jury that convicted two former top officials of the Roger Williams Medical Center for paying a state senator to advance the hospital’s agenda.

Prosecutors filed an 81-page brief at the First Circuit Court of Appeals in Boston yesterday in the cases of Robert A. Urciuoli, Roger Williams’ former president and chief executive officer, and Frances P. Driscoll, a senior vice president.

Urciuoli, who faces three years in prison, was convicted in October of conspiracy and 35 counts of mail fraud. Driscoll, who faces eight months in prison, was convicted of one count of mail fraud. Both are free on bail pending appeal.

Prosecutors alleged Urciuoli and Driscoll hired state Sen. John A. Celona, a Democrat from North Providence, to a sham job at an assisted-living center and nursing home affiliated with Roger Williams. But Celona’s $700 to $1,000 weekly salary was really meant as payment to kill bills that were adverse to the hospital’s interests and to otherwise look out for the hospital legislatively, prosecutors charged.

Driscoll and Urciuoli appealed their convictions, arguing that Judge Ernest C. Torres gave faulty instructions to jurors before deliberations. A key complaint was that Torres did not tell the jurors to limit their consideration to Celona’s official duties and votes at the State House. Instead, Torres told jurors they could consider anything Celona did “under the cloak of his office.”

In their filing yesterday, prosecutors said that Torres did nothing wrong and that case law supports his actions.

pparker@projo.com