I don't know where the truth lies exactly except that police shot two dogs, including one dog who was chased - yes, chased - for an hour before being shot to death.
In the first story, a mixed breed dog is shot in the leg after apparently lunging at an officer. The dog had been running loose and acting in a "threatening manner" and so police were called in. According to police, they tried macing the dog but the dog still "lunged" and so the dog was shot.
The second story is more tragic. A dog got out of her yard and was running loose. For over an hour, they chased this scared, frightened dog. I don't know the details but it sounds like that the dog was not acting aggressive but scared. She was running away. And she was still shot 2-3 times and killed.