A recent notification indicates that, with effect from October 1, 2013, U.S. visa applicants from State of Bihar will fall under the Consular District of U.S. Consulate in Kolkata. Previously, they were covered under the jurisdiction of the U.S. Embassy in New Delhi. Since there is no restriction based on geographic location, U.S. visa applicants can continue to apply from anyone of the five U.S. visa processing posts in India. However, the notification encourages residents of Bihar to apply from the U.S. Consulate, Kolkata.
This notification can be found here.