A 26-year-old woman from Burnley was arrested on suspicion of the concealment of the birth of a child contrary to Section 60 of the Offences Against the Person Act 1861.
A man aged 30 has also been arrested on the same charge after police discovered the body of a newborn baby at an address in Burnley just before 3pm yesterday (Monday).
Officers attended an address at Wellington Court in the town where they found the body of a newborn baby, a police spokesman said.
The death is currently being treated as unexplained.
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Police inquiries are continuing.