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They have accused troops of abducting and murdering the men, police said on Friday.
"We're investigating the matter," Deputy Inspector General of Police S S Bijral told Reuters.
An army spokesman declined to comment on the FIR.
The three men were gunned down last Saturday when, the army said, they were crossing the Line of Control from Pakistan.
The army alleged that the trio belonged to the Pakistan-based Harkat-ul-jehdai-islami and took reporters to see the bodies laid out beside a large pile of arms and ammunition.
But the villagers said the dead men were a father, son and son-in-law who lived nearby.
They had even complained to visiting Union Minister of State for External Affairs Omar Abdullah, son of Jammu and Kashmir Chief Minister Farooq Abdullah, police said.
"He has taken a very serious note of the incident and has taken the matter up with authorities," a police official said.
Earlier this year, the state government admitted that officials had manipulated forensic samples in an attempt to prove the guilt of five youths blamed for the massacre of 36 Sikhs two years ago ahead of a visit by then US President Bill Clinton to India.
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