Md Mohiuddin, chief of Kachua Police Station, said that the accident occurred around 8:30 am on Thursday in the Biswa Road area of Kachua Upazila.
The dead were identified as Urmi Majumder Uma, 24, Saddam Sohen, 35, and Md Rifat, 24.
The injured were identified as Md Ibrahim, 25, of Baliatoli Village and autorickshaw driver Monir Hossen, 30, from Nichchitpur
Police said the Hajiganj-bound autorickshaw overturned after being hit by the Dhaka-bound BRTC bus from Kachua, leaving three dead on the spot.
Police and locals rescued Monir and Ibrahim and took them to a local hospital.
Monir was taken to Cumilla Medical College Hospital for advanced treatment after receiving first aid at the Kachua Upazila Health Complex. Ibrahim is being treated at the Kachua health complex.
Kachua Upazila Health Officer Salahuddin Mahmud said Monir was referred to Cumilla Medical College as his condition deteriorated.
OC Mohiuddin said the police recovered the bodies of the three victims and brought them to the police station. The BRTC bus has been taken into custody.
The incident will be investigated and legal action will be taken, Mohiuddin said.