Baby Charlotte Lukendlay died four days after being rushed to the Launceston General Hospital on February 21, 2016.

The inquest, before Coroner Olivia McTaggart, heard the baby suffered a hypoxic brain injury and fractures to her ribs consistent with multiple separate instances of trauma prior to her death.

Charlotte's father, Gaurav Endlay, spent about 40 minutes in a bedroom alone with the baby the night she became unresponsive, the court heard.  

More on the inquest:

The baby was taken by ambulance to the LGH and then flown to the Royal Hobart Hospital. 

The court heard Mr Endlay drove his wife, Rongrong (Angel) Lu, to the Hobart hospital as they were unable to fit in the air ambulance. 

Mr Endlay did not go inside the hospital to check on his daughter when the couple arrived, instead he started driving back to Launceston to finish packing boxes for the family's move to Wagga Wagga in NSW. 

A doctor from the RHH called Mr Endlay to advise him to return to the hospital as his daughter's condition was serious.

The inquest heard conflicting evidence about the phone conversation, with Mr Endlay denying he had to be convinced by a social services employee to drive back to the hospital. 

While giving evidence on Thursday, Mr Endlay told the court about two events he had not told police in either of his interviews.

He told the court when the couple was outside the LGH after finding out their daughter would be flown to the Hobart hospital, Ms Lu was crying on his shoulder and was nervous. 

He told her not to worry because "nothing is going to happen to you. I said put things on me',".

Ms Lu was given time to question Mr Endlay during Thursday's proceedings and, in reference to him saying put things on him, she asked what made him think they were in trouble.

Mr Endlay said it was because Ms Lu was so nervous. 

Ms Lu told the court she had no memory of the conversation.  

Coroner McTaggart told Ms Lu that counsel assisting Rebecca Lancaster had pointed out "inherent difficulties" with the conversation Mr Endlay spoke about. 

The court also heard there was an incident about 20 days before baby Charlotte went to the hospital where she also had difficulty breathing. 

Mr Endlay told the court Ms Lu put the baby on her stomach then took a phone call and walked outside. 

"I picked her up and she was not breathing normally," he said. 

Mr Endlay said he called Ms Lu to check on the baby, but neither called an ambulance. 

Ms Lu denied the incident took place. When asked why he didn't tell police, Mr Endley said he "couldn't say that to police at the time".

The inquest was adjourned.