Another election, in Lower Saxony, is expected to result in a win for Christian Wolff, the CDU-aligned state premier who rules in a coalition with the Free Democrats.
The CDU won 43.8 per cent of the vote in the northern state, according to projections by ARD television, taking a commanding lead over the SPD, which took 29.6 per cent.
The left, a combination of former Social Democrats and ex-communists, won 6.6 per cent in Lower Saxony, ARD said.
Such a result would be enough to enable the party to enter the state legislature for the first time.
Wulff has distanced himself from Koch's hardline policy suggestions.
Koch has campaigned for tough new measures to tackle youth crime, prompting a hostile reception from immigrant groups who have accused him of racism.
By early afternoon, 34.6 per cent of the 4.37 million eligible voters had cast ballots in Hesse, while only 22.65 per cent of the 6.1 million voters had turned out in Lower Saxony.
The elections come as Kurt Beck, SPD leader, looks to dismantle reforms brought in by Merkel's predecessor Gerhard Schroeder, a centrist Social Democrat.
Victory for the SPD would encourage them to push further for the introduction of a national minimum wage.
The mimimum wage proposal is popular with the German public but has been called potentially harmful to jobs by many economists.
Support for Koch has dropped by more than 10 per cent in the last few weeks, after he held a double-digit lead in the polls.
Koch recently called for tougher policies on young criminals from immigrant backgrounds, after a highly publicised attack on an elderly German man by two men, one Turkish, one Greek.
The strategy has been strongly criticised by immigrant organisations and Yspilanti.
"You cannot put out a fire by pouring oil on it," a group of prominent members of Germany's 2.5-million strong Turkish community said in an advertising campaign in major newspapers.