Satyajit Kumar Ghosh, assistant superintendent of police (Raipura circle), said supporters of Ashraful Islam and Ratul Hasan Zakir, an independent candidate, attacked each other in front of Bashgari UP complex around 6:00am, two hours before the beginning of the elections.
The two groups fired gunshots and attacked each other with teta (a type of fishing spear), leaving three people dead and 30 others injured, he said.
The injured were taken to Brahmanbaria and Narsingdi Sadar hospitals.
On information, police rushed to the spot and brought the situation under control.
Additional police have been deployed in the area to avert further trouble.
However, voting is underway in Bashgari union parishad.
Polling began in 835 of 848 UPs at 8am on Thursday and will continue till 4:00pm.
More than 41,000 candidates, including 3,310 contenders for the post of chairman, are contesting in the countrywide second phase UP election.
A total of 81 chairman candidates have already been elected unopposed. Similarly, all contestants -- for chairman and member posts, and reserved seats -- in five UPs were elected uncontested.
Some 28,747 candidates are contesting for the member posts and 9,161 women for the reserved seats in the UPs.
But 203 member candidates and 73 women candidates for reserved seats were elected unopposed in this phase.
There are nearly 16.6 million voters -- 8,405,831 men, 8,189,379 women and 16 transgender (hijra) -- under 8,492 polling stations in these UPs.