BBC News reports that officers were called to a flat in Wolverhampton on Saturday after reports of a missing child.
Police found what they describe as a 'very young baby' with serious injuries in a rubbish collection area.
The baby is currently in Birmingham's Children's Hospital in a critical condition.
A 24-year-old woman has been arrested on suspicion of attempted murder, and 32-year-old man is being questioned on suspicion of assisting an offender.
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