Sue the Hell out of the city and it’s Jack Booted Thug “Police” “force”!
Can't - sovereign immunity. However, I would make sure I got the officer's name and maybe a picture and publish them far and wide - local paper and tv news, web sites, etc. I'd be sure I shamed him publicly - a police officer who couldn't handle a family pet without killing him.
Sue the hell out of the cowardly officer and toss him out of the force.
“That officer later explained to the family that he was following procedure.”
They were just following procedure.
Step 1] Attempt to save escaped tiny dog from harm.
Step 2] If Step 1 fails, frag it.
Step 3] Call the proper authorities that you should have called before attempting Step 1.