Roy Allison, 65, was found hanged in the grounds of the city crematorium on Sunday, hours after the body of 36-year-old Duncan Bell was found stabbed.
Police have confirmed they are studying a letter but would not reveal details.
The Peterborough Telegraph said it was one of 14 recipients of the nine-page letter on Tuesday.
The letter states: "Like he did my son, I will do to him and take it all away from him. I take my own justice."
The body of Duncan Bell, of Winyates in Orton Goldhay, was found at a house on the nearby street of Hetley on Sunday.
Police have said they are not looking for a suspect and have linked the stabbing to the death of Mr Allison, who was found at 08:30 BST on Sunday.
Peterborough Telegraph editor Mark Edwards told the BBC he opened the letter at the newspaper's offices on Tuesday afternoon, and immediately called police.
The newspaper had by that point reported on the two deaths, and in March had covered the death of Mr Allison's son, Ray Jr, 28.
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