Police said the child's grandmother, who was the only person present near her when the incident occurred, is "not in the best of mental health" to properly recall the incident.
"The child's grandmother is quite old and isn't in the best of mental health. She was the only one present at the time of the incident and sometimes she is saying that someone came and fed her something while other times, she is saying that something fell on her. We are investigating the matter," said a senior police officer.
"I leave my house at 8 AM and return around 9.30 PM. I do not interact with many people and have no enmity with anyone," he said.
His wife had gone to the terrace to get the clothes when the incident happened on January 21.
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The baby is admitted at Safdarjung Hospital and has started recovering.
"She has burn injuries on her face and was not able to intake anything. Today her condition is a little better. She is playing and is a little better," her father said.
"I am the only earning member in the family. The treatment costs are difficult for me to manage. But yesterday a policeman gave me Rs 2,000 for the treatment," her father said.
"The family belongs to Farukkhabad in Uttar Pradesh and the baby's father says he will take her to his village, but we are trying to dissuade him from it because the child won't get this kind of treatment there," said the officer.
The baby also has an elder sister and their father is worried about the family's safety.