Kelly Burns, from Lincoln, says X-rays show an air rifle-style pellet lodged in her pet's jaw.
The force has been assessed as having "widespread or systemic performance concerns" in a new report.
Inspectors rated Lincolnshire Police "inadequate" at investigating reports of child abuse.
Lincolnshire Police warns against taking in the animal after finding one in 'squalid conditions'.
Lincolnshire Police is appealing for witnesses to help with its investigation.
Lincolnshire Police has been given an addition £28m but it is still facing a "dire" situation.
Coasters and posters are given out to pubs as studies show domestic violence increases during games.
Lincolnshire Police says it will also boost its staff numbers and create a new fraud team.
Former PC Alan Kirkwood would have had a final warning if he had still been a serving officer.
