The incident happened on Sunday at a remote tribal hamlet Paisaramkarbaripara, about 120 km from the state capital, when a villager refused to allow a man to stay at his house for the night, with a woman who had earlier sought refuge, the Superintendent of Police (SP), Sudipta Das, said.
The episode triggered a war of words between the ruling BJP and the opposition Congress.
The Congress claimed that all the three deceased were its supporters, and that they were killed by BJP cadres.
"Three Congress supporters were brutally beaten up and murdered. Two others are hospitalised in critical condition, while another is missing," Tripura Congress vice-president Tapas Dey said on Monday.
The SP, meanwhile, ruled out any political link with the incident.
Trouble started after a 40-year-old woman, who came to the village to take part in the traditional Biju festival, sought shelter at the house of the local resident, since she could not go back home at that hour, Das said.
Soon after, a 19-year-old man demanded to stay the night at his place, and in the woman's room, the SP said.
When the owner of the house refused to oblige the man, the latter caught hold of an axe and allegedly killed him, his father and the woman, Das said.
The man has been arrested.
The Congress has also lodged a complaint with the returning officer of the East Tripura (ST) constituency, which will go to polls on April 18.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)