Justice Loya was hearing the Sohrabuddin Sheikh encounter killing case in 2005, at the time of his death.
The Left party, in a statement, said many recent media reports have highlighted the anomalies in the judge's death.
Family members of the deceased judge had in a recent media interview claimed that attempts were made to bribe and intimidate Loya during the course of the trial.
"The whole matter has raised disturbing questions of murder, bribery, subversion of law and manipulation of institutions of parliamentary democracy at the highest level, which must be seriously investigated," the CPI(M) asserted.
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