The Colorado Supreme Court, which barred former President Donald J. Trump from the state’s primary ballot, is composed of seven justices who were all appointed by Democratic governors.

Justices on the court serve 10-year terms, and Democrats have held the governor’s office for the last 16 years, so all of the current justices were appointed by that party, with five appointed by one man: John Hickenlooper, who was governor from 2011 to 2019 and is now one of the state’s U.S. senators.

Still, the chief justice, Brian Boatright, is a Republican, while three justices are Democrats and three are listed in voter registration records as “unaffiliated” with a party.

And the court was not of one mind on whether Mr. Trump should appear on the ballot. The decision was 4-3, with the court ruling that the 14th Amendment forbade Mr. Trump from holding office because he had “engaged in insurrection” on Jan. 6, 2021, when his supporters overran the Capitol. (Of the four who voted with the majority, two are registered Democrats and two are not registered with a party.)

The decision was harshly criticized by supporters of Mr. Trump, who said that keeping him off the ballot was undemocratic. The head of Colorado’s Republican Party, Dave Williams, said “out-of-control radicals” in Colorado “would rather spit on our Constitution than let the people decide which candidates should represent them in a free and fair election.”

But some observers of the court say that it is notably nonpartisan, in part because of how the justices are named. The governor must choose from a pool of nominees recommended by a bipartisan commission. The majority of the members on that commission are not lawyers. Still, most are chosen by the governor.