File a police report. Document document document.
File a complaint against the officer.
If nothing else, the dog should be impounded for 10 days as a bite case at the owners expense and should be tattooed as a dangerous dog.
The dog attacked you and yours on your property.
If you can stand it, go to the police station to file the report and make sure you get a case number and then go to animal control to file a report. It doesn't really matter what caused the the bleeding. it occurred while you were struggling with an aggressive dog, so if skin was broken it is certainly considered a bite case.
File a complaint against the animal control moron.
DO NOT LET THEM TRIVIALIZE THIS EVENT. What would happen had it been a small child attacked and not your pet?
What on earth are these people thinking - no - clearly they are not thinking and are being lazy public servants who are trying not to do their jobs.
What a couple of retreads!
I'm so sorry you had to suffer through this. I'm so sorry your hand and pet are injured.
Best wishes to both of you.