Agnihotri had contacted a placement agency in south Delhi's Haidarpur a month ago and paid Rs 16,000 for providing a domestic help, a senior police official said.
The agency, claimed to be owned by Ranjit Mandal and Shankar Mandal, provided the top official with a domestic help at his AB-93 Shahjahan Road residence.
According to the complaint filed by Agnihotri, the domestic help reached his residence on June 27 morning and was with the family throughout the day till they went to sleep.
"She slept earlier in a separate room. However, in the morning of June 28, when we woke up around 6:30 am, we found that she had left the house without our knowledge," the official said.
Following investigations, police registered a case of cheating and criminal breach of trust has been registered against the Mandals.
The capital has witnessed similar cases in the past and several such agencies were smashed.