Under the Indiana code: "A person who observes a dog in the act of killing or injuring livestock may kill the dog if the person has the consent of the person in possession of the real estate on which the dog is found." On the other hand, if the person put others at risk he could potentially be liable for unlawful discharge of a weapon. I would report it to the police/sheriff and animal control. I would also want some proof that your dog was in fact killing his turkeys.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
Whether your dog is vicious, with or without question marks, is irrelevant. The issue is whether your dog was on your neighbor's property, attacking his domestic animals.
IF so, the Indiana statute already cited (and hardly unique to IN) sanctions the action. If not, you have a claim for damages and, possibly, the shooter may be in violation of IN animal cruelty laws.
The case would come down to who could prove where the dog was and what it was doing when shot. You may wish to retain an animal law attorney and review the case with him/her.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
The first thing to do is report this to the police and local Animal Control to investigate. If your dog was on his property and was going after his turkeys, unfortunately, he may be in the right. You will need to determine where the dog was when he was shot. This is very important. Did your dog have permission to be on the owner's property? There is not a simple answer to your problem.