Was the other dog leashed? If the other dog was leashed and you let your dog go, you probably don't have a very strong case. Moreover, unless the vet bills are astronomical, it would not make economic sense to file a lawsuit. Try talking it over with the neighbor; I'm sure he/she feels very bad.
You can also report the incident to animal control if you believe the dog is dangerous.
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It is difficult to tell based on your answer. There are important issues, such as where this happened. However, you share liability by letting your dog loose. You can try to file a criminal complaint, especially if the dog has killed before. You may want to ask the neighbor if they are willing to share in the vet bill. Another option is small claims court.