The force confirmed yesterday that the buzzard was found dead in the lower part of Hound Hill Lane, Barnsley, with trauma to its head attributed to either a pellet or shot projectile.
Police Constable Mark Winter, Penistone Community Constable and Wildlife Crime Officer. said: "Buzzards, being part of the Bird of Prey family are protected in law and it is quite obviously an offence to shoot, injure or trap one.
"This incident has occurred over the last few days and this is an appeal for information to assist with this investigation. Wildlife Crime will not be tolerated in our County, please enjoy the Countryside safely, responsibly and leave it as you found it.
"PC 403 Mark Winter, Penistone Community Constable and Wildlife Crime Officer."