Jonathan Percival was born on 25th November 2014 but pronounced dead a short time later.
The Rev Jim Percival, the vicar of Holy Trinity Church of England Church in Freckleton, Lancashire, and his daughter, Ruth were both questioned on suspicion of murder.
Police were called to the vicarage in the early hours of the morning following a report that a woman had given birth to a stillborn baby.
The pair were initially bailed pending further inquiries but in January this year, Lancashire Police retained the pair once again for questioning over child neglect.
Mr Percival's wife, Susan, 66, was also held in late 2014 on suspicion of conspiracy to conceal the birth of a child.
No further police action or prosecution was taken on any of the individuals questioned.
A full inquest, scheduled to last three days, will begin later today at Blackpool Coroner's Court with the full post-mortem report expected to shed some light on the baby's death.
By Dan Golding