MONTPELIER, Vt. — The second-place finisher in last month’s election for governor announced Monday that he is staying in the race, bucking recent history of the losing candidate conceding and leaving the final say up to the state Legislature.

Speaking at the Statehouse, Republican Scott Milne criticized what he called the “pervasive incompetence” of Democratic Gov. Peter Shumlin’s administration and described the state’s finances as “a disaster.” He rattled off a litany of complaints, including the lack of a plan to fund the state’s proposed single-payer health care system, the failure to implement a law requiring statewide prekindergarten and the absence of a plan to clean up Lake Champlain.

“I would consider the record of the incumbent in judging whether his record justifies the blessing of a vote for the office,” Milne said. “I would weigh his promises against his performance. No one earns another term, but performance must serve as a measure of fitness.”

In a statement, Shumlin reiterated that he was the top vote-getter in the election and that he expected the Legislature to return him to office.

“I continue to believe that the Legislature will honor the long democratic tradition of electing the candidate who received the most votes,” Shumlin said in a statement. “Since the election over a month ago, I have continued to work hard to put together a legislative agenda and budget to address the challenges facing our state.”

The Vermont Constitution requires the governor, and some other top offices, to receive more than 50 percent of the vote to be elected, or the Legislature gets the final say. Traditionally the losing candidate concedes, and the vote is a formality. The secret-ballot vote during a joint session of the House and Senate will be held Jan. 7, the first day of the 2015 session.

Milne, a travel agent from Pomfret, was a latecomer to the election and given little chance of winning. But Shumlin, a two-term governor, got 46.4 percent of the vote in the Nov. 4 election and Milne got 45.1 percent.

The Democratic Party controls 106 of the 180 seats of the Vermont House and Senate.

House Speaker Shap Smith, D-Morristown, said Monday that the election is required by the Constitution regardless of whether Milne participates.

“My expectation is historical precedent will be followed,” Smith said.

David Sunderland, the chairman of the Vermont Republican Party, said the party would fully support Milne but noted that the makeup of the Legislature made it difficult for him to win.

“But he’s been facing an uphill battle since the day that he announced that he was running for governor, so I would be hesitant to say that anything is out of the realm of possibility for Scott Milne,” Sunderland said.