Three members of a family Bandhuprakash Pal, his wife Beauty and their eight-year old son Angan were found murdered in their residence in Jiaganj on Tuesday.
Following the murders, the Bharatiya Janata Party (BJP) and the Rashtriya Swayamsevak Sangh (RSS) had claimed that Bandhuprakash regularly attended Milan, a weekly programme of the RSS, for the past few months.
"We have not arrested anyone till now. We had detained four persons, but freed two of them after interrogation. We are questioning the other two," Murshidabad Superintendent of Police (SP) Mukesh Kumar told mediapersons.
Asked about the police findings, he said: "We are getting some financial dealings and are working on that. Once we are confirmed, we will let you know."
In a series of tweets, the state police said that investigation into the triple murder case started "just after the incident".
"Prima facie it seems to be a case of personal enmity and it has nothing to do with politics," the police said in another tweet.
"Two persons have been detained and are being examined. The probe has found that the deceased person was also working as an agent of some insurance and chain companies and was in a serious financial crisis.
"His family members have denied affiliation with any political group. A diary note found suggests serious differences in the family," the police said.
Meanwhile, the Criminal Investigation Department (CID) of the state police has been asked to get associated with the investigation.
Noted filmmaker Aparna Sen has described the incident as "shame" for the people of the state, asking Chief Minister Mamata Banerjee to ensure that the perpetrators are brought to justice.
"Pregnant wife & child of RSS man slaughtered in our own WB! Whatever the reason for such a gruesome act, shame on us! Madam CM! Pls ( Please) Aensure the perpetrators are brought to justice! Irrespective of political inclinations, all citizens of WB are ur (your) responsibility. U (You) are CM to all," she tweeted.
The incident has also triggered slugfest between West Bengal Governor Jagdeep Dhankhar and the ruling Trinamool Congress.
While the Governor on Thursday condemned the incident as "dastardly and barbaric", the ruling Trinamool gave a strong counter alleging that Dhankhar was "transgressing his constitutional jurisdiction."
The Governor in a strong statement said the incident has "shocked the conscience" on account of its enormity and it was "reflective of intolerance and worrisome law and order situation" in the state.
"Why such canards are being spread about an incident in Murshidabad? We feel that to cover up the infighting of the BJP, the office of the Governor is being used. The Governor is transgressing his constitutional jurisdiction by making such comments," said Trinamool heavyweight and state Education Minister Partha Chatterjee.
( With inputs from IANS )