The deceased were identified as Jamal Hossain, and his mother Kamala Begum, 70, residents of the same area.
The tragic incident took place around 12 noon.
Jamal received a massive electric shock as he was trying to save his cow which was electrocuted in a room of his house, police and eyewitnesses said.
"During the sudden rain, the cow ran into the room where a battery-powered auto-rickshaw was charging. While running, it inadvertently collided with the auto-rickshaw and was electrocuted," the sources added.
In the meantime, Jamal's mother rushed to the spot and tried to rescue her son but got electrocuted and died on the scene.
Mostakim Islam, in-charge of the Goral Police Investigation Center in Kaliganj, confirmed the matter, reports BSS.