By The Cockroach Janta Party called a Sansad Chalo march to Parliament on July 20.
It demanded the resignation of the then Education Minister Dharmendra Pradhan over the NEET-UG paper leak.
Violence broke out during the march.
The Delhi Police Crime Branch has now begun a probe into that violence.
The reports did not include a response from the CJP.
The probe will examine whether the violence was premeditated or whether criminal elements infiltrated the march after the CJP called for it.
Police are also checking whether WhatsApp or Telegram groups were used to mobilise people, according to The Week.
The alleged offences include assaults on police personnel, vandalism and damage to public property, including police vehicles.
They also include obstructing government employees and snatching police equipment such as jackets and helmets.
Police used facial recognition data to identify 2,873 suspects with criminal backgrounds, according to the police sources quoted.
The reports do not say how many of those suspects were involved in specific acts, and they do not say how many have been arrested or charged.
A criminal background does not by itself show that a person took part in the violence, and individual roles are still being examined.
Investigators have reviewed more than 250 videos, including mobile phone recordings, CCTV, drone visuals and police body-worn camera footage, according to The Week.
The July 20 Sansad Chalo march demanded the resignation of the then Education Minister Dharmendra Pradhan over the NEET-UG paper leak.
Security was tightened at Parliament and several entry gates were closed on the day, according to The Daily Jagran.
The Daily Jagran reported that videos showed assaults on women protesters and stone-pelting by protesters.
It also reported that police used lathi charges, water cannons and pellet guns, which caused widespread uproar.
The Supreme Court ordered that no coercive action be taken against student protesters over the FIRs, according to The Week.
Parliament building, New Delhi (file image), Wikimedia Commons, GODL-India
