PROVIDENCE — Agonizing over the guidance given by the law and the courts, the state Board of Elections last night voted 3 to 1 to deny Bernard A. Hawkins’ bid for a new election in the five-way race for Smithfield Town Council.

In the seventh hour of a marathon meeting, the board certified the election of Republican Maxine A. Cavanagh by a 39-vote margin, 4,151 to Hawkins’ 4,112.

In other contested races, the board certified the election of James A. Seveney to the Portsmouth Town Council and Richard Buonauito to the East Greenwich Town Council.

In Burrillville, Debra L. Stockwell was elected to the School Committee. And in Tiverton, the board certified Philip A. DiMattia as town treasurer.

Legal arguments in the Smithfield case revolved around ballots printed in error with the name of Richard A. DiIorio, a Democrat like Hawkins, who had dropped out of the council race weeks before the November election.

Vice Chairman Frank Rego said he was inclined to grant Hawkins’ bid because inconsistencies in the printed ballots put some voters “in a different election” than others.

Board member Richard Pierce argued against a new election, citing a state law which says that the names of candidates who have died or withdrawn after a certain date, like DiIorio, need not be removed from the ballot. Their votes are simply not counted.

Initially, opposing motions by Rego and Pierce failed for want of seconds.

Board member Martin Joyce Jr. said he was torn between the arguments.

“I agree with both,” he said.

Joyce asked for guidance from the board’s lawyer, Raymond A. Marcaccio.

Marcaccio said the law allows a ballot to list the name of a candidate who has withdrawn or died, but it does not anticipate the printing of more than one ballot for the same election.

At the same time, Marcaccio said, he did not hear Hawkins’ lawyer pinpoint a specific due-process violation that prompted the candidate’s call for a new election.

Hawkins was represented by Angel Tavares, who maintained that the inclusion of DiIorio’s name hurt Hawkins.

A new election would address a high probability of error in the outcome, Tavares said.

He emphasized that there were a high number of irregularities — in the hundreds — in proportion to the double-digit spread between Cavanagh and Hawkins.

Ultimately, Joyce voted with Pierce and Chairman John DaLuz against a new election.

The board labored for six hours last night on the first-ever count of ballots that contained either too many votes or no votes. The Rhode Island Supreme Court recently ordered the board to review these ballots for voter intent rather than let voting machines accept them or reject them.

In Portsmouth, Seveney edged out Joseph W. Robicheau by 22 votes, 3,746 to 3,724.

Burrillville’s Stockwell edged out Peter F. Lambert by 22 votes.

Tiverton’s new treasurer, DiMattia, won by 52 votes against Laura Epke.

And in East Greenwich, Buonauito’s margin against Steven W. Gregson was 28 votes.

gmacris@projo.com