The case was lodged on Thursday after an order was passed by Chief Judicial Magistrate Surya Kant Tiwari two months ago on a petition filed by local advocate Sudhir Kumar Ojha.
"The CJM had passed the order on August 20, accepting my petition upon the receipt of which an FIR was lodged today at the Sadar police station here," Ojha said, according to a News 18 report.
Ojha said signatories of the letter were named as accused in his petition, in which they allegedly "tarnished the image of the country and undermined the impressive performance of the Prime Minister" besides "supporting secessionist tendencies".
The police said the FIR was lodged under sections of the Indian Penal Code, including those relating to sedition, public nuisance, hurting religious feelings and insulting with an intent to provoke breach of peace.
The letter was written by 49 personalities, including filmmakers Mani Ratnam, Anurag Kashyap, Shyam Benegal, veteran actor Soumitra Chatterjee and vocalist Shubha Mudgal in July this year.
The letter had stated that the lynching of Muslims, Dalits and other minorities must be stopped immediately, while stressing that there was "no democracy without dissent". It also noted that the chant "Jai Shri Ram" had been reduced to a "provocative war cry".