In the first incident, a short-eared owl was shot and killed shortly after 8pm on September 11 on Wessenden Head Road.
Police are looking to speak with the driver of a dark coloured pick-up truck, described as having two dog cages on the back with a thick wooden cover over the dog cages, which was seen in the area at the time.
The second shooting was of a tawny owl on the Kirklees Way footpath, just off nearby Greenfield Road, on about October 1.
A post mortem has since confirmed that the bird had been shot before being stuffed into a dry stone wall.
West Yorkshire Police is working with the Royal Society for the Protection of Birds (RSPB) on the investigation.
PC Darren Parkinson, Rural Crime Officer for Kirklees, said: “We have been carrying out a number of enquiries into these shootings and have been liaising with the RSPB as we have progressed our investigations.
“We would like to speak with anyone who has information about either offence or may be able to identify the vehicle described in connection with the first shooting.
“Owls, along with all wild birds, are protected under the Wildlife and Countryside Act 1981 and it is a criminal offence to kill or injure any wild bird. The government has set persecution of birds of prey as one of their wildlife crime action priorities.”
Anyone who has information about the crimes is asked to contact West Yorkshire Police on 101, quoting crime number 13180457435 for the shooting of the short-eared owl or crime number 13180516301 for the shooting of the tawny owl.
PC Parkinson can also be contacted by email at [email protected]