Detectives said a man captured and killed the bird about 5.30am on George Street before approaching members of the public as they walked past and threatening them with the dead bird.
Police attended and spoke to a man at the scene but are appealing for anyone who witnessed the incident or may have footage to contact them.
However, he said it may be difficult to bring animal cruelty charges against the man responsible.
"It will have to be taken into account whether the bird died immediately or suffered," he said.
Mr Beatty said if the animal died quickly then it would make pressing animal cruelty charges "more complicated".
However, if witnesses came forward with evidence the bird suffered, the likelihood of charges would increase.
District Duty Officer Senior Sergeant Neville Mills said police take matters of animal cruelty extremely seriously.
"Attacks of this nature will not be tolerated and those responsible will be dealt with to the full extent of the law," he said.
Mr Beatty said the year had not started well after more than 90 animals were seized from an alleged puppy farm west of Stanthorpe on Monday.
(Hawkesbury Gazette - Jan 21, 2017)
