The letter, received by the office of the judicial magistrate in the district court, Gyanendra Tripathi, is signed under the name of Lashkar-e-Taiba.
A worried Tripathi handed over the letter to district police chief Manjil Saini who in turn ordered a probe into the matter.
Saini asked a special police team to ascertain from where the letter was dispatched and also to verify it.
Security around the office of the judicial magistrate has been enhanced, an official said.
A case was filed in June against Jammu and Kashmir Chief Minister Omar Abdullah in the district court after he made some statements on Article 370 that grants special autonomous status to the state.
The case is likely to be heard soon.