A delegation of the BJP leaders led by former state Law Minister Suresh Kumar met Bengaluru Police Commissioner T Sunil Kumar and filed the complain accusing Mr Siddaramaiah of branding BJP and RSS members as "terrorists".
On Wednesday, Mr Siddaramaiah provoked massive outrage as he likened the BJP, its ideological mentor RSS or Rashtriya Swayamsevak Sangh to terrorists, hours after he was described by the BJP as "anti-Hindu".
"Whether it is the Popular Front of India (PFI), Social Democratic Party of India (SDPI), Bajarang Dal, Vishwa Hindu Parishad or any other organisation... if they indulge in disturbing harmony and brotherhood in the society, and spread communalism, they will not be tolerated," he said.
Mr Siddaramaiah's comments quickly escalated into a raging controversy with the opposition party in the state accusing him of trying to polarise voters on communal lines ahead of polls later this year.
Mr Rao had gone a step further by calling the BJP and the RSS a terrorist organisation. "They kill people, ask them to migrate to Pakistan and openly claim that they would change the Constitution by saying this they are becoming a terrorist organisation," Mr Rao had said.
The BJP and the Congress have been involved in war of words after Uttar Pradesh Chief Minister Yogi Adityanth's rally in Bengaluru.
Yogi Adityanath, seen as the BJP's Hindutva mascot, had targeted Mr Siddaramaiah for remembering his Hindu roots. "Just as Congress President Rahul Gandhi went to temple after temple during the Gujarat election," he taunted.