BERLIN — Voters in one of Germany’s most prosperous states punished Chancellor Angela Merkel’s conservatives again on Sunday in an election that was seen as yet another barometer of her and her party’s standing with the German public.

The verdict in Hesse state, an apparently tepid, and certainly shrinking, well of support for the chancellor’s party, was in keeping with the trend throughout Germany in recent years.

While Ms. Merkel’s Christian Democrats emerged as the leading vote getters and were expected to be chosen to form a new government there, that was hardly surprising. They have dominated politics in Hesse state for nearly two decades, sometimes by wide margins.

But in the voting Sunday, the conservatives were expected to earn the backing of only about 27 percent of the ballots — more than 10 points less than in the previous election in 2013.