They beat up Assistant Sub-Inspector Imrul Kayes and Constable Mozammel in broad daylight and stripped them naked at Dyarkanda village in Kalmakanda upazila.
Villagers said the policemen had come to the local market on a motorcycle.
Kayes and Mozammel, who were not in uniform, demanded Tk20,000 from stone trader Al Amin, saying he was accused in a case and threatened to arrest him if he did not comply.
Amin left the spot pretending to bring the sum and informed the villagers about the extortion bid.
Agitated locals surrounded the policemen and at one stage, physically assaulted the duo and stripped them naked. They also vandalised the motorcycle and snatched a pair of handcuffs from the policemen.
ASI Kayes and Constable Mozammel fled the scene. They could not be reached for comments.
Kalmakanda police station OC Abu Bakar Siddique said he had heard about the incident. “We will investigate the matter first,” he said, declining further comments.
Netrakona's police chief Joydev Chowdhury said they would take administrative action against the duo if they were found guilty.