Bandopadhyay, the spokesperson of West Bengal Congress unit, was arrested on Thursday evening by the Purulia district police from his home in North 24 Parganas district.
The killings took on a political colour when the BJP slammed the state government over the incident and claimed that the man was its supporter.
Dhankhar, who had been recently involved in a war of words with the state government, said he is acting within the parameters of the Constitution.
TMC will soon bring a no-confidence motion against the present board of the Bhatpara municipality, party senior leader Jyoti Priya Mullick said.
Shah, also union home minister, had told a news channel during the day that BJP is going to form the government in West Bengal with two-thirds majority in the 2021 assembly polls.
Officials said the Union home ministry has directed the Central Reserve Police Force to take charge of Dhankhar's security that will be valid in all parts of the country.
The development comes in the backdrop of the BJP making deep inroads in Bengal and placing itself as the main challenger of the ruling Trinamool Congress.
Bengal BJP president Dilip Ghosh took out a rally on the occasion from Karnogarh to Matkatpur-Inda at Kharagpur in West Midnapore district.
Referring to the Bengal police cracking the Murshidabad triple murder case, Trinamool Congress secretary general Partha Chatterjee criticised the BJP for trying to politicize a heinous crime.
Banerjee had launched on July 29 a helpline number and a website didikebolo.com as part of the outreach programme on the advice of poll strategist Prashant Kishor.
BJP general secretary Kailash Vijayvargiya said his party also took the matter of the murder of three members of a family to the President.
Jagdeep Dhankhar's statement came three days after his comment that a triple murder in Murshidabad reflects the 'worrisome' law and order situation of the state had not gone down well with TMC.
Senior Congress leader Abdul Mannan had met Gandhi at her residence in New Delhi twice on Thursday evening and discussed the political situation in the state.
Nusrat participated in the ritual popular among women devotees at a pandal here on Friday evening as part of Vijaya Dashami celebrations.
While the CM was seated in a gallery with bureaucrats and ministers, Dhankar and his wife took their seats in another gallery.