On Sunday, voters in hundreds of cities, towns and villages across Germany’s most populous state will choose their next local officials.

Although the elections, in North Rhine-Westphalia, have no direct effect on national politics, many in Germany are watching them as a measure of the country’s mood. They are the first electoral test for the Christian Democratic Union party of Chancellor Friedrich Merz since he assumed office in May.

Since Mr. Merz won the national election in February, the far-right Alternative for Germany party, or AfD, has continued to surge in popularity, with polls showing that a quarter of voters back it.

The AfD, which Germany’s domestic intelligence service has designated an extremist party, is now neck and neck with Mr. Merz and his conservative alliance, which won 28.5 percent of the vote but whose support has fallen to 26 percent, according to polls.

The center-left Social Democrats, who are the junior partner in Mr. Merz’s government coalition, are faring even worse.

Here is what to know about the vote on Sunday.

How will national politics affect the vote?

Polls for the races in North Rhine-Westphalia either do not exist or are unreliable, so it will became clear only after ballots are counted on Sunday night whether Mr. Merz’s governing coalition in Berlin has hurt or helped the Christian Democratic Union in the state elections.