Officers said they wanted to empower people to act against militants who have killed dozens of secular activists, Hindus and other minorities across the country in recent years.
Arrests in Bangladesh anti-militant drive top 8,000
"We want to change the scenario. We want the people to be cautious, safe and united against militancy and other crimes," said Ehsan Ullah, police chief in the western district of Magura, which has a large Hindu population.
Ullah said the sticks and whistles were aimed partly at raising morale among local people.
"Almost all recent (militant) attacks took place during a time when roads were empty and the local community was busy with farming or asleep," he told AFP.
Police denied the scheme could be open to abuse, despite concerns from some human rights activists that the move could trigger mob lynchings.
Bangladesh arrests 37 'Islamist militants' in crackdown
The Islamic State group has claimed responsibility for the Hindu priest's murder and other recent attacks.
But authorities instead blame homegrown militant groups and say IS and other international group have no presence in Bangladesh.
Last Friday the police launched a crackdown on militant groups in Bangladesh in the wake of the violence, arresting more than 11,000 people in recent days.
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