Investigators said they have identified a crucial link and a woman named Lakshmi is being questioned.
The baby Falak was admitted to AIIMS with severe injuries and is battling for life after a teenaged girl, who was looking after her when her boyfriend left the girl with her, got her admitted.
A senior police official claimed one Munni along with her daughter had come to Laxmi's house in September last year claiming that her husband has abandoned them.
Laxmi asked her to stay in her house.
The official said Munni disappeared from Laxmi's house after 20 days leaving the child there.
"Laxmi then gave the child to Manoj who entrusted the girl with Rajkumar who was living with the teenaged girl who allegedly beat the baby girl," the official said.
Rajkumar allegedly took the child to his house in November but his wife refused to keep the child.
"It was during the time Rajkumar met the teenager. He then started living with the teenager and the girl. Mid-January, he left for Mumbai to get his physically- challenged son treated. The teenager was taking care of the baby. It appears that she coud not take proper care of the child and out of frustration she assaulted her physically," the official said.
A police team sent to Mumbai is yet to locate Rajkumar.