So I did some googling and like most things, "it's complicated."
It varies by state, but killing a police dog can put you in jail for 10 years (and this has happened) and that is a federal law. There are some states pursuing stricter measures themselves where killing a canine officer is equivalent to killing a human officer.
As to what I said about killing a police dog having a harsher punishment, that was based on a single anecdote and I meant that the judges serve harsher punishments, not that the laws themselves are stricter.
https://www.deseretnews.com/article/900010289/senate-approve...
https://abcnews.go.com/US/story?id=96229&page=1
https://www.wpxi.com/news/local/man-who-killed-pittsburgh-po...