The districts that went to the polls are East Champaran, West Champaran, Gopalganj, Saran, Siwan and Vaishali.
"The turnout was nearly 55 percent and nowhere less than 50 percent. The polling was peaceful," a senior police official told IBNS after the polling ended.
There was no major untoward incident.
Earlier, Director-General of Police Neelmani said a constable, found in an inebriated condition at Gopalganj town, was detained for causing inconvenience to the voters.
"The elections, however, by and large were peaceful," Neelmani said in the afternoon.
In Bettiah Assembly constituency, where state Bharatiya Janata Party (BJP) minister Renu Devi is in the fray, voters did not turn up at booth Nos. 119 and 120 as they have decided to boycott the polls due to 'the state's apathy towards their woe'.
One of the key contestants in this phase was former chief minister Rabri Devi who fought the polls from Raghopur in Vaishali district. She is also in the fray from Sonepur constituency.
Rabri Devi's brother Sadhu Yadav, who had parted ways with the RJD and joined Congress, also contested the polls in this phase.
He contested from Gopalganj as a Congress candidate.
Meanwhile, three Rastriya Janata Dal (RJD) leaders from Patna have been expelled on Thursday for alleged anti-party activities.
State RJD secretary Anil Yadav, Pappu Yadav and Rampravesh Rai have been expelled by the party's state president Abdul Bari Siddiqui. They have been accused of working against Ramanand Yadav, who is the party's official nominee from Fatua Assembly constituency.