Police Commissioner M. Mahender Reddy said a team from Central Crime Station (CCS) will conduct an inquiry into both the incidents.
"We will take appropriate action against whosoever is found guilty," he told reporters after visiting the Maredpally police station, which was ransacked by about 200 people late on Monday.
Police have also picked up few people involved in the attack on the police station, in which two sub-inspectors of police and a homeguard were injured.
Angry over death of Bandappa, 53, his family members and relatives attacked the police station, ransacked and set afire the furniture and three two-wheelers parked in the premises.
A personal computer, files and furniture were gutted in the fire. The protestors also damaged a police patrol vehicle.
The attack led to tension in the area. Police deployed additional forces and Rapid Action Force (RAF) as a precautionary measure.
Bandappa's relatives alleged that he died due to police torture. However, police suspect he might have died of overdose of alcohol or due to illicit liquor.
Deputy Commissioner of Police N. Prakash Reddy said the man was drunk when he was arrested during Bonalu procession on Sunday. The officer said the cause of death would be known after the inquiry.
Bandappa was arrested as he picked up an argument with a homeguard and created nuisance during the procession. He was released from the police station on Monday. The family took him to a doctor as he complained of uneasiness. He died on his way to Gandhi Hospital.
The attack on the police station took the police by surprise. There were only a handful of policemen at the police station as most of the personnel were deployed for security arrangements during Bonalu festival.