The inquiry headed by Inspector General (Konkan Range) Sukhvindar Singh commenced today with the officer visiting the local police station in Palghar.
Police said Singh sought details of the FIR copy and police diary after briefly speaking to officers at the police station.
The inquiry was ordered by Maharashtra government following the public outrage over the arrest of two girls for posting comments on Facebook.
Shaheen Dhada and Renu Srinivasan, both aged 21, were arrested on Monday morning over their post opposing the Mumbai shutdown, but were granted bail after they furnished personal bonds, police said.
Dhada allegedly posted that one should not observe bandh for Thackeray's funeral. "We should remember Bhagat Singh and Sukhdev," the post said. Her friend Renu was arrested for 'liking' the post.
Protesting Dhada's post, suspected Shiv Sena workers vandalised the clinic owned by Dhada's uncle Abdul, a member of the Indian Medical Association.
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Palghar police arrested 10 suspected Sena activists and produced them before a local court which granted them bail on a personal bond of Rs 7500 each.
"About 30 to 40 unidentified people are still wanted in the violence case. We will arrest them soon," said Srikant Pingle, Senior Inspector at Palghar police station.