At a news conference in Hamilton, Minogue said he would ask Oliver to resign if the Republican ticket wins in November. Oliver “will not be my lieutenant governor,” Minogue said, adding that he was glad Oliver was safe but disappointed in his judgment.

Oliver, a New Bedford city councilor, was arrested late Saturday after his SUV reportedly struck five parked cars and overturned. He was charged with operating under the influence of liquor, negligent operation of a motor vehicle, speeding and a marked-lanes violation. He pleaded not guilty Monday in New Bedford District Court and was released on the condition that he not drive while the case is pending. His next court date is Nov. 16. Police said no one else was seriously injured.

The Republican ticket’s names are already on ballots, and more than 200,000 people had voted early by Monday, according to Minogue. He urged voters to vote for him as printed and not cross out Oliver’s name or write in another candidate, warning that altering the ballot could disqualify the vote.

Massachusetts has no process for a governor to appoint a replacement lieutenant governor or call a special election if the office becomes vacant. The position would remain unfilled until the next regular election. That happened during the final stretch of Gov. Deval Patrick’s tenure, after Lt. Gov. Tim Murray resigned.

The lieutenant governor can act for the governor when the governor is out of state and has other duties, including presiding over the Governor’s Council. If the office is vacant, the secretary of state is next in the line of succession, followed by the attorney general, treasurer and auditor.

Asked whether he was ready to take on duties assigned to a lieutenant governor, including chairing the council, Minogue said he would rely on experienced people around him. He said some members of his prospective team, like him, would volunteer rather than take a salary.

Oliver joined Minogue’s ticket after Minogue won the Republican primary. Minogue said he had supported Anne Brensley for lieutenant governor at the party convention, but she did not submit the signatures needed to qualify for the ballot, citing allegations of fraud by a signature collector. Oliver was the only lieutenant governor candidate on the September primary ballot.

Minogue said Oliver’s not-guilty plea did not change his decision. “For what has happened alone,” he said, Oliver could no longer serve as his lieutenant governor.

Minogue also framed his response as an example of political accountability and contrasted it with Democratic Gov. Maura Healey’s handling of a former aide arrested on alleged cocaine-trafficking charges. Healey said she fired the aide after learning of the arrest. A recent UMass Amherst/WCVB poll cited in the report put Healey 25 percentage points ahead of Minogue.