X-rays taken of the buzzard found at the end of August revealed it had been previously shot three times.
Pellets were found embedded in the bird, which had also suffered recent injuries to its head consistent with being confined in a cage trap.
The trap was not found and police are not giving away the exact location of where the bird was found apart from saying it was in the western area of the East Riding
Wildlife Crime Officer PC Brandon Ward is appealing for information. He said: "However this bird met its end it has previously been shot.
"Raptor persecution is a National Wildlife Crime priority which we take very seriously. Whatever anyone's feelings are towards birds of prey there is no excuse for this type of criminality.
"It's sad that such practices are still common place. Due to the nature of these crimes they are difficult to detect.
"If you have information about anyone persecuting birds of prey we want to know.
"I can be contacted in confidence via 101 and your information will be treated with the utmost confidentiality."
It comes days after the annual Birdcrime report which showed North Yorkshire remains the worst blackspot in the country for bird of prey persecution - with nearly a quarter of all confirmed incidents happening in the county.
However also listed were three incidents in East Yorkshire - involving two poisoned buzzards and one shot sparrowhawk.
The charity says the figures" only scratch the surface of the true extent of raptor persecution in the UK."