The Delhi Police has already arrested a man in connection with the case after Mr Hashmi reported the matter to the Commissioner.
The newly-appointed chairman of Delhi Minorities Commission, Zafarul Islam Khan, confirmed the notice to Delhi Police in connection with the threat received by Mr Hashmi.
He also said a forensic test was needed to pinpoint the man who threatened Mr Hashmi over phone.
"I have issued a notice to the Delhi Police, through the Commissioner of Police, for a fair investigation into Shabnam Hashmi's matter," he said.
Mr Hashmi, founder of the NGO Pehchan, had complained to the Delhi police commissioner Amulya Patnaik that the man who threatened her identified himself as sub-inspector Sandeep Malik from the Lajpat Nagar police station.
The woman's auto rickshaw driver husband Mohammad Haseen had got a call from the number asking him to appear at the Lajpat Nagar police station.
Mr Hashmi said that when she called on the given number to know the reason for summoning Mr Haseen, but was met with abuses from the other side. She also said that she was threatened to be killed in an "encounter". The call was recorded by her.
The Minorities Commission chairman said "(It needs to be ascertained) if the arrested man is the real accused. Only a forensic test will reveal whether it was him who threatened Mr Hashmi or it was someone else."
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