Midwives had repeatedly warned the mother about the risks, but the mother ignored the 'safe sleeping' advice she was given before she left hospital and regularly slept with the baby between her and her partner.
In July last year she woke to find the baby had stopped breathing and called an ambulance, but paramedics could not save the child. Officials launched a full investigation as the parents were known to social services.
The baby - named only as Child W - was born healthy in May 2011 at University Hospital, Walsgrave, according to the report to Coventry City Council.
The child had not been taken into care but staff decided to carry out a further family assessment. Last week the city's safeguarding children board published its report, which found the baby's death could not have been prevented.
However, health chiefs said this wasn't an isolated tragedy and are warning parents against putting their babies to bed next to them.
Across Coventry and Warwickshire 27 babies have died in their parents' beds since 2008.
Carmel McCalmont, head of midwifery at University Hospital, said all pregnant women and new mothers were advised against co-sleeping.
However, she said some parents continued to do so, often because they were tired or had been given poor advice by relatives.
She said: "Babies should sleep on their back with their feet to the bottom of the Moses basket or cot.
"No matter how tired parents are they should never be tempted to bring their baby to bed with them.
"Drinking alcohol and being very tired are significant risk factors because parents can sleep so deeply that they roll over and can suffocate their baby.
"Also, a lot of parents think they are doing the right thing by going outside to smoke. They don't realise the toxins remain on their clothes. We advise to avoid smoking."
Some charities continue to promote the benefits of co-sleeping, such as making it easier for mums to breastfeed, but one organisation in the US ran a hard-hitting campaign saying the practice was as dangerous as a baby sleeping with a meat cleaver.
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