You have a right to file a police report each and every time there's an incident. If they refuse to take it, tell them you'll call the Attorney Generals Office and the Feds and will file a formal complaint against their PD for not doing their job.
It is their responsibility to look into the matter - regardless of how ill staffed they may be!
It is their responsibility to protect it's citizens - regardless of how "innocent" they think the act may be! It's called harassment and it's against the law!!
What they're doing to your animals is called animal cruelty and that's also against the law!!!
There's a sociopath running loose in that town and it's their responsibility to track him/her down.
Also, if this is a child - teenager - underage person - doing all this, the PARENTS need to be held accountable for their little heathens act of vandalism. There needs to be restitution for the damage done (vet bills, ads you've run to track your dog down, repairs made due to damage, etc) I don't care if it's the Mayor's kid. I don't care if it's a policeman's kid. Whoever this may be, they need their hiney's kicked into next year!
You're feeling threatened. That's the bottom line. The PD can either get it together and do something about this or they can be left open for a lawsuit. (hint at that as well)