Dungannon Crown Court heard on Friday that the pair were asked at the time what had happened the infant.
Rachael Martin, the baby's mother, repeatedly ignored the question while her former partner Barry McCarney said: "I found her like this".
McCarney, from Woodview Crescent, Trillick, who denies murder, is also accused of sexually abusing the infant girl.
He is further charged with unlawfully and maliciously causing the child grievous bodily harm, and causing her death by an unlawful act.
Rachael Martin, from Main Street, Kesh, is accused of failing to protect her daughter from the unlawful act that caused her death, and wilfully neglecting her in a manner likely to cause her unnecessary suffering.
Nursing staff at the Erne Hospital in Enniskillen also claimed that the pair, while distressed and agitated, seemed to keep their distance from one another.
It was also claimed that at one stage McCarney "was concerned that he had to get home to get changed".
However, staff said that McCarney later claimed that when he went to check on baby Millie, he thought the infant wasn't breathing, and while Rachael reported that her daughter had "flu like symptoms" that day and was "lethargic", she kept wanting to be reassured that her child would be "alright".
The infant was pronounced dead in Belfast's Royal Victoria Hospital for Sick Children, on 11 December 2009.
However, a consultant has already claimed the infant was already brain-stem dead by the time she was treated at her local Co Fermanagh hospital.
Staff Nurse Sinead Doyle said when the infant was admitted to A&E she "appeared limp and lifeless".
She said she asked McCarney, who had rushed in bare-foot with baby Millie in his arms, what had happened, but he only replied that he was "the partner".
The night duty nurse, Silvia Love, said when Baby Millie was rushed in, the infant was "unresponsive, very grey, very pale and there was a small cut, or nick on the bottom of her left lip".
She claimed McCarney told her that "he normally checked the child nearly every hour and a half".
He added later when asked how he found the child, he said he "felt the child was lifeless and there was no response".
Nurse Love said he then told her "he brought her (the child) downstairs, he shook her and proceeded to give her mouth to mouth," before running to a neighbour to get a lift to the hospital.
"He said she wasn't breathing," added the nurse.
She said that McCarney appeared "very agitated", but was "concerned that he had to get home to get changed" because he had a "mark" on his sleeve, although she could not say what it was.
Nurse Love added that while a crying Martin had her "mother for comfort and reassurance", she became "hysterical" when told her infant daughter had to be helped with her breathing.
Later under cross-examination, Nurse Love agreed that when first interviewed by police she had made no mention McCarney saying he found baby Millie "lifeless and there was no response".
She also agreed that Martin, when told of the treatment being given to her daughter, not only became hysterical, she asked: "What, she's not breathing for herself?"
Ward Sister Betty McCleery said when an "unkempt" looking Baby Millie, with "long straggly hair " was admitted, "lifeless and pale", she was "immediately worried and extremely concerned".
Sister McCleery claimed that in the intensive care family waiting room, "their body language appeared as if they were in disagreement" and that while McCarney sat on one chair, Martin sat across from him, "with her back to him".
The trial continues on Monday.