The counting of votes began at 08:00 local time (02:30 GMT) on Friday.
Trends are expected to become clear by noon local time, although the counting will finish only by evening.
The Bihar polls serve as a precursor to several other key state state elections next year in West Bengal, Kerala and Tamil Nadu, where the BJP is not in power and has struggled to make inroads.
Bihar, with more than 74 million voters, is India’s poorest state, with millions migrating to other parts of India for jobs. It is also among the few states in India where Modi’s party has not managed to form a government yet on its own.
The outgoing government is an alliance between the BJP and the Janata Dal (United).
Both the parties contested the recent election together, while India’s main opposition Congress party tied up with the regional Rashtriya Janata Dal (RJD) and several smaller parties.
The polls also witnessed the entry of a new political party led by Prashant Kishor, a former political consultant who has in the past worked with both the BJP and the Congress.
