Police found the body of a new-born baby at a property in the town.
Officers had been called shortly before 3pm on Monday to reports of a sudden death at an address in Wellington Court.
A 30-year-old man and a 26-year-old woman, both from Burnley, were later arrested on suspicion of the concealment of the birth of a child contrary to Section 60 of the Offences Against the Person Act 1861.
The pair were released without charge yesterday.
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Following an initial post mortem, the baby was found to have a number of injuries which require further examination.
The man and woman were both re-arrested today on suspicion of murder and are currently in custody.
Det Chief Insp Jill Johnston, of Lancashire Police, said: “This is a tragic incident involving the death of a new born baby girl in Burnley.
“My thoughts are with the family and friends of those affected at this sad and distressing time.
“Following extensive enquiries we have re-arrested two people on suspicion of murder.
“This remains a complex investigation and a team of specially-trained officers are conducting a number of enquiries.
“We are urging anyone who has any information which may assist with our investigation to contact police.”
Anyone with information can contact police on 101 quoting log reference 0703 of January 16.
Alternatively Crimestoppers can be contacted anonymously on 0800 555 111 or online at Crimestoppers-uk.org.