Granted it stinks when a neighbors dog kills your birds...
...and the neighbor should keep their dog confined according to local laws.
BUT
It's also your responsibility to keep your birds safe by keeping them within a secure fence.
This is the better long-term approach. Law enforcement and neighbor sentiments will be reactionary only in most instances. You will also have other dogs and wild predators eventually as well. Make certain those chickens are staying on your property, if not this discussion is a waste of time.
SSS is already not good option because of unpleasant discussions. You will be suspected and very likely treated harshly.
You need to get past this as not a good start as a forum topic.