A protected bird of prey was shot and fatally wounded in the Forest of Dean.
Two people heard a shot and saw the kestrel fall to the ground just outside Newent on 12 January, Gloucestershire Police said.
Officers said the bird was taken to a wildlife hospital but had to be put down.
PC Cath McDay, of the force’s Wildlife and Rural Crime Team, said it was “unacceptable behaviour” and appealed for witnesses to contact police.
Birds of prey are protected by law under the Wildlife and Countryside Act.
PC McDay added: “Someone has broken the law in shooting this protected bird of prey, which sadly could not be saved.
“This is unacceptable behaviour and I’m asking for anyone with information to contact police.”