In his letter, CPI(M) general secretary Sitaram Yechury also referred to media reports claiming members of a cow vigilante group were involved in the "barbaric" act and pressed Singh for "most urgent" action in the matter.
"Please treat it as most urgent and take necessary action as the Haryana government and its administration appear to be indifferent and insensitive in the matter. I am aware that law and order is a state subject in the Constitution.
Yechury's letter was based on a report by a team of CPI(M) leaders who visited Dingerheri village in the Mewat district on August 30.
A couple was murdered and two girls from the family allegedly gang raped after the accused had barged into their house in the wee hours on August 25.
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On August 28, Haryana Police had arrested four youths in connection with the incident.
After committing the crime, the accused had tied the injured with ropes and escaped from the spot. Some residents living nearby found the injured after which the police was informed.