"We have registered an FIR under Indian Penal Code (IPC) sections 295 A and 298. We are investigating and verifying the facts," the official told .
IPC Section 295 A deals with deliberate and malicious acts intended to outrage religious feelings and Section 298 deals with uttering words and other actions aimed at hurting religious feelings.
The FIR was registered against the school's governing council members Kalladka Prabhakar Bhat, Chinnappa Kotiyan, president Narayana Somayaji and convener Vasanth Madhav.
The Popular Front of India (PFI) filed the FIR on Sunday evening.
None of the people named in the FIR were summoned by the police for questioning but the official said they will be served a notice for questioning if need be.
Meanwhile, the police are trying to find out the people responsible for producing the Babri Masjid demolition skit.
As Bhat is from the Rashtriya Swayamsevak Sangh (RSS) and influential, the police are also factoring in the law and order situation before proceeding.
Surprisingly, many students who participated in the same programme where the Babri Masjid image was demolished are Muslims, official said.
According to police, many Muslims students attend Srirama Vidya Kendra for education and several Muslim families and students were present in the event on Sunday night.
"We have to get the statement of the people who witnessed the programme," an official said.
Manguluru is not like other parts of Karnataka, as it is communally very sensitive where complaints and counter-complaints between communities is common place, the official said.
Kalladka, where the school is located, Surathkal and Bantwal villages are also communally sensitive, he said.
Many complaints about communal disharmony end up being fake and exaggerated in the region, with police receiving hundreds of complaints, officials said.
Puducherry Lieutenant Governor Kiran Bedi on Monday shared videos from the school event where students mimicked demolishing an imaginary Babri Masjid.
( With inputs from IANS )