The case was lodged following an order by Muzaffarpur Chief Judicial Magistrate Surya Kant Tiwari on a petition by local advocate Sudhir Kumar Ojha, who claimed, among other things, that the letter supported secessionist tendencies".
"The CJM had passed the order on August 20, accepting my petition upon the receipt of which an FIR was lodged at the Sadar police station here," Ojha said.
He said nearly 50 signatories to the letter were named as accused in his petition, which accused them of having "tarnished the image of the country and undermined the impressive performance of the prime minister", besides "supporting secessionist tendencies".
The letter was written by 49 eminent personalities, also including filmmakers Mani Ratnam, Anurag Kashyap, Shyam Benegal, actor Soumitra Chatterjee and vocalist Shubha Mudgal in July this year.
It said that the lynching of Muslims, Dalits and other minorities must be stopped immediately, while stressing there was "no democracy without dissent".
It also noted that the 'Jai Shri Ram' slogan was reduced to a "provocative war cry".
Rahul Gandhi, who was away in his constituency Wayanad in Kerala, denounced the FIR.
"Everybody knows what is going on in the country. It's not a secret. In fact, the whole world knows it. We are moving into an authoritarian state. It's pretty clear," the Wayanad MP, who was in his constituency to express solidarity with those protesting the night traffic ban on the highway passing through the Bandipur Tiger Reserve, told reporters.
"Anybody who says anything against the prime minister, anybody who raises anything against the government, is put in jail and is attacked. Media is crushed. Everybody knows what's going on. This is not a secret," he added.
Filmmaker Aparna Sen chose not to comment on the development.
"Sorry, no comments. The matter is subjudice," she told PTI when reached for reaction.