The incident occurred in Cassiobury Park, at around 7pm last Friday (16 April).
It was reported that the deer had been chased by two lurcher-type dogs, which were not on leads. While trying to escape, the animal became caught on fencing, sustaining injuries.
Officers attended to try and free the deer, but it managed to run off of its own accord and could not be located.
Enquiries are being carried out to try and trace the owner of the dogs.
PC Jenny Edwards, from the constabulary’s Rural Operational Support Team (ROST) said: “We are currently working to establish the circumstances around what happened and would ask anyone who saw the incident to contact police. We’re also keen to trace the owner of the dogs; if this was you, or you know who it is, please get in touch.
“I’d also like to take this opportunity to remind people of their responsibilities while out walking dogs in public places. Please ensure you are familiar with legislation around when and where dogs are required to be kept on leads.”
Anyone with information about the incident is asked to please email firstname.lastname@example.org