The sparrowhawk was found severely unwell in woodland near Kirbymoorside in Ryedale and taken in to a local vet for care.
After suffering seizures and clenching its talons, the bird was unable to recover and died shortly after. Police have said its symptoms were typical of birds which have been poisoned.
It follows a spate of birds of prey in the county being killed after ingesting poisonous pesticides, with police believing these may have been deliberate acts.
Earlier this year, a spaniel was killed after ingesting pesticides while out on a walk with her owner in Pateley Bridge in Nidderdale.
Subsequent tests showed the presence of four different pesticides in the spaniel's body, the combination of which are known as the "Nidderdale cocktail" and have been found in the bodies of birds of prey found poisoned in the area.
The sparrowhawk found in woods near the village of Gillamoor earlier this month is to be tested by the Wildlife Incident Investigation Scheme (WIIS), which will determine whether pesticides were involved in its death.
A spokeswoman for North Yorkshire Police said: “At this time, we are keeping an open mind as to the cause of death. However, toxicology results may not be known for a number of weeks, so we want to make the community aware so they can take precautions to keep pets, children and themselves safe.
“Once the results of the tests are known we will update the community, but for the time being dog owners should take care to keep their dogs on leads when in this area, and remain vigilant.”
Police have also warned the public not to directly touch birds or other animals which may have been poisoned, as poisons can transfer through contact with skin, and instead take a photograph and a precise location before contacting the force.
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