An investigation was launched after a dead buzzard was found on February 1 in woodland near the River Skell in High Skelding near the village of Grantley in Nidderdale.
Police arranged for an x-ray at a local vet, which showed the bird had been shot. It is thought to have been shot between January 31 and February 1
A North Yorkshire Police spokesman said: " Buzzards, along with all wild birds, are protected under the Wildlife and Countryside Act 1981 and it is a criminal offence to kill or injure any wild bird."
Call police with information on 101, quoting crime reference number 12170018791.