Avon and Somerset Police said they are working closely with West Mercia Police "to explore any potential links" between the murder of the Reverend John Suddards in Thornbury, South Gloucestershire, last week and the murder of Betty Yeates, 77, in Bewdley, Worcestershire, last month.
Stephen Farrow, 47, who was wanted over the death of clergyman Suddards in his vicarage in Thornbury, has been arrested on suspicion of murder early Sunday morning.
Avon and Somerset Police wanted to talk to Farrow in connection with the death of Mr Suddards in his vicarage in the South Gloucestershire town of Thornbury on Tuesday.
Police announced that a 43-year-old man arrested on Tuesday in connection with the crime had been freed on bail.
Mr Suddards was found stabbed to death at his home in Castle Street in Thornbury on Tuesday morning. The alarm was raised by workmen who arrived at the vicarage next to St Mary's Church and found it was locked.