I would buy some type of blue tooth spy camera and wear it whenever you are outside so you can record the guy’s words and actions. You need it to be conveniently on you and ready to go in a hands free position that can video your interaction with him.
I am sorry you have to go through this.
You could always give this a try. 
Also, don’t ask to speak to the Chief unless he is one of two officers where you live or no one does anything at all to help you. If there is one thing that is going to make the guys who will actually handle the situation think you’re a self important cry baby it is circumventing the normal process for making complaints and attempting to go right to the chief without giving them a chance to do their jobs. Inevitably if you do get through to the chief all he will do is relay 1/3 of what you told him to a patrolman and tell him to handle it or he will relay 1/3 to a lieutenant who will relay 1/3 of that to a sergeant who will relay 1/3 of whats left to the patrolman who will handle the complaint.
OP, I feel for you. As I read through the thread I’m thinking of the ways I’m labeling this first call - Threats, Animal Call, Disturbance - Noise, Disturbance - NonViol, Misc Incident/Info. And you need to make that call to PD immediately while the action is in progress.
Then I’m thinking the guy would get ED’d if he flips out while PD is on scene with him.
I’m thinking if he ever comes on your property while you’re there how you’ll want to request a CTW from the PD you called out there the second you saw him come over.
I’m thinking how you do need to report the verbal threats to the PD. He is already physically abusing the dog, he is already physically damaging property, how long until he snaps off on you?
In short, you need to call the PD so that you can start that History at that location. It doesn’t take long before a location is known to have ‘one of those’. And there’s at least a few in every jurisdiction. On first contact the PD is going to run him and it’s possible the guy has warrants. They could take a ride right then. Point is, you put the guy on the PD radar. Chances are things will escalate over at that house. If it isn’t you it might be a different neighbor, maybe a young mom who is an easier target for the guy to scare. Who knows, he might lose his marbles while PD is talking to him and they’ll take care of it quick, fast and in a hurry right then and there.
But first off, the guy needs to be put on PDs radar.
I wish you luck Euro, a lot of good advice has been given. I lived in Chicago while going to tech school in an apartment, heard a lot of disturbance next door and never did anything about it as far as contacting authorities, until one evening my future wife and I were leaving to go watch a movie to walk out the door and find our neighbor standing there with both wrists slit asking for help. Don’t put this off. Get the ball rolling ASAP to do something about it. My wife and I helped save that womans life (the hard unforgettable way) she wanted to end so bad from being beaten all the time, I pray I never have to live that again. It could have been stopped so much sooner.
Glad we moved out of the burbs, I have no neighbors close enough to hear what’s going on now. Best of luck, stay safe.
Story 1: Officer, I’m a quiet guy, law abiding, mind my own business, and this guy across the back fence yells and screams and beats his dog. He has hopped up on my fence and threatened my life and my dog. I’m afraid for my safety.
Story 2: Officer, the gun nut who lives behind me has a long range camera and keeps snapping pictures of my poor mentally challenged young son. He records us and violates our privacy, and I think he has an arsenal in there because he’s always carrying a gun. I’m afraid for my and my son’s safety.
Very good point of view here.
I think if the officer were to get Story 2, your doing a lot of things wrong.
Jus make the call already. I’ve lived through this crap a few times and the longer you wait the further they’ll push it. Then it gets blurry for the cops. They won’t know what to believe and meanwhile the other guy becomes violent and/or passive aggressive (usually both) against you, your property and your dog. Lots of ways to kill a dog and ruin your shit without a shred of proof. Next thing you now you’ve made your own property off limits to yourself and just stay inside just to keep anything from starting, trapped in your own home. Anything left out, like a vehicle or even lawn furniture magically gets vandalized as soon as you turn your back. It escalates damn far, damn quick over nothing.
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Call the police every time he acts nuts and when the dog barks. They will quickly see he has issues. If he acts the way he did with you I’m sure they will handle it appropriately.
Eurodriver, have you been in contact with the police yet? You really need to start a paper trail on this guy for when he finally does something violent. People with his issues start with pets. Some, not all, move to abusing/assaulting other people.
The OP has requested that this thread be closed for a bit.