The bird was found dead by officers on July 12 at Barden near the Strid, on the Bolton Abbey estate.
North Yorkshire Police yesterday said the force was now examining whether the bird had flown to the site after being shot, or if it was shot close to where it was found.
Sergeant Kevin Kelly, wildlife crime lead for North Yorkshire Police, said: “We have commenced an investigation and aim to establish the circumstances leading to the bird’s death.
“What we know at this time is that a triage x-ray shows a small piece of shot inside the bird.
"This will be recovered and forensically tested. We will be working with partner agencies and the Bolton Abbey Estate to establish the facts that will assist an effective investigation.”
Doug Simpson, from Yorkshire Red Kite organisation, said the latest death brings the total number of Yorkshire red kites killed up to 42, since records began in 1999.
Thirteen of those birds were shot, he said.
Mr Simpson added: It is sickening that a small minority of people appear intent on breaking the law by targeting these birds, which have become an integral part of our beautiful North Yorkshire countryside.”
Benedict Heyes, from the Bolton Abbey Estate, said he was notified by a member of the public that they had found the dead bird on the Bolton Abbey Estate.
“Red kites and other birds of prey are often seen at Bolton Abbey and are enjoyed by many visitors to the estate," he said.
"The estate alerted the authorities and would ask that anyone who has any knowledge or information in relation to the death of this bird to contact North Yorkshire Police, so as to assist them in their investigation.”
Anyone with any information is asked to contact police on 101, quoting reference number 12180131874.