The jury heard the mother, who has name suppression, had traces of alcohol and prescription drugs in her blood stream just hours after her daughter died.
A forensic scientist told the court that based on a blood sample taken hours after the baby's death, she believed the woman's blood alcohol level could have been three times the legal driving limit.
She also said the woman's blood contained the drugs zopiclone and methadone, which are known to make people sleepy.
Earlier, the jury heard how the mother took drugs before breastfeeding just days after the birth of her baby.
A witness, whose name and profession are suppressed, said the mother told her she had taken drugs within days of the baby's birth.
The witness said she told the mother several times not to drink while breastfeeding, but the mother continued to do so.
The jury was also told the mother confessed to feeling responsible for her baby's death hours after she died.
The witness said the mother was distraught the day the baby died, repeatedly saying she had killed the baby.
The witness also told the court the mother had consumed alcohol that day to build up the courage to ask a relative for money.
Another witness has described to a jury the day she discovered a Taranaki mother unconscious and smothering her baby.
The mother is on trial in the High Court at New Plymouth, for the manslaughter of her baby in February last year.
The third witness of the day said she came to check on the mother, when she discovered her crouched over and asleep in her home.
The witness, who has name suppression, said the mother's other child had to wake the mother up when she arrived.
As the mother sat up she noticed the baby was underneath her, and the 6-week-old had turned yellow and wasn't breathing, the court heard.
The witness said she called an ambulance straight away, but the baby was unable to be revived.
