Lawyers for former President Donald J. Trump filed an appeal on Tuesday seeking to overturn the ruling last week by Shenna Bellows, Maine’s secretary of state, to bar him from appearing on the state’s Republican primary ballot.

Ms. Bellows, a Democrat, “was a biased decision maker who should have recused herself and otherwise failed to provide lawful due process,” lawyers for Mr. Trump wrote in the 11-page appeal filed in Maine Superior Court. They further argued that she had “no legal authority to consider the federal constitutional issues presented by the challengers.”

Ms. Bellows “made multiple errors of law and acted in an arbitrary and capricious manner,” the lawyers wrote. They demanded that the court vacate the secretary’s decision, which they described as “the product of a process infected by bias.”

Maine became the second state to exclude Mr. Trump from the primary ballot on Dec. 28, when Ms. Bellows found him ineligible under the third section of the 14th Amendment, which prohibits people who have engaged in insurrection from holding office. Her decision followed a similar landmark finding in Colorado, where the state’s supreme court ruled on Dec. 19 that he could not appear on the ballot there.