The BJP says it is a dangerous precedent to provide prestigious post-retirement posts for the heads of investigating agencies like the CBI or the NIA. (Watch)
The party says that if the country's most senior investigators believe that during or after exiting office, they are eligible for other high-profile jobs, the neutrality of their offices could be compromised because they may seek to please the government.
Sources within the BJP also suggest that the party's senior leaders feel they cannot support Mr Sinha's appointment to the NHRC because of the NIA's focus on right-wing terror cases.
The government last evening over-ruled the BJP. Mr Sinha's nomination to the NHRC, a body with nine members, has to be formalised by the President of the country.
Members of the NHRC have to be selected by a committee which includes the Prime Minister, Home Minister, Leaders of the Opposition in both Houses of Parliament, the Speaker of the Lok Sabha and Deputy Chairman of the Rajya Sabha.
The BJP plans to send a letter of dissent to the committee, which means its stand would be on record. Arun Jaitley, Leader of Opposition in the Rajya Sabha, wrote, "Heads of investigative agencies must function without fear or favour... It is this temptation of a future favour which is seriously compromising the functioning of heads of investigative agencies."
The issue will also become a point of battle when the budget session of Parliament resumes on April 22.
The BJP had recently opposed the appointment of former CBI director AP Singh to the NHRC.
The opposition and the government had disagreed three years ago about the appointment of PJ Thomas as Central Vigilance Commissioner. The BJP said that because Mr Thomas faced allegations of corruption in Kerala, he should not have been considered for the position.
The government disagreed but in March 2011, the Supreme Court nullified Mr Thomas' appointment.