Manju Devi, 22, died after delivering a boy at the Community Health Centre in nearby Farah village yesterday, they said.
When the villagers learnt about her death, they protested outside the facility.
Rup Singh, her husband, alleged that the centre's staff had told him to take her to the district hospital.
"A departmental probe has been ordered into the matter," S K Tyagi, the chief medical officer, said.