Ms Bairagi's family has said that they want stern action to be taken against Dr Vasantrao Pawar Medical College, located in Nashik's Adgaon area. The hospital is run by an education society, the Maratha Vidya Prasarak Samaj.
The hospital has denied the allegations, saying it was "impossible" for a cockroach to have remained alive inside the ventilator.
"When the hospital staff put her on ventilator support, a new filter-tubing had been placed then," the hospital's superintendent Dr Ajit Patil told PTI.
While not denying the relatives' allegation of finding a cockroach inside the ventilator, Dr Patil said that they had only found it after Ms Bairagi's death.
"The cockroach was spotted in the ventilator by her relatives nearly an hour after it was switched off," he said.
Ms Bairagi's body was later sent for a postmortem to Nashik Civil Hospital.
Her family carried out her cremation afterwards. It was unclear why Ms Bairagi had consumed poison.
(With Inputs From PTI)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.