I would do a little digging to determine what the state/local law is on dogs 'hazarding' livestock. And pay particular attention to exactly how 'hazarding' is defined.

If the sheriff is called in by a dog owner, as unlikely as that might be, you want to start the interview with the right words. Words that make it clear that yes, the dog/s were clearly a legally 'substantial and imminent' threat that fulfills the requirements for use of lethal force.

Words that make it clear that you are very careful how you shoot, what you use to shoot, what direction you shoot, and making clear that you are well aware of sight lines and the potential for bullets to carry over considerable distances.

I'm not saying that you lie. I am saying that you need to be careful how your case is presented. Police are trained to testify in court in a manner that makes it perfectly clear that a checklist of requirements has been mentally checked off before they used force.

A good example of this is a homeowner that shoots someone in their home needs to avoid talking about wishing/desiring/acting to kill or punish the intruder and any reference to the intruders race of status. Those are part of what normally goes through the mind but the laws doesn't allow you to act on those thoughts so it is better if they are not mentioned. In most situations you are only allowed to use lethal force if you are in fear for your life and to eliminate that clear and imminent threat.

Get it clear in your mind that you were in fear of clear, imminent and credible threat, and have on the tip of your tongue a laundry list of signs of why you were in fear and how you acted only to eliminate this credible threat.

How you present the situation, particularly in the initial presentation to the law, makes the difference between a open and shut case, and a protracted investigation and seating of a grand jury that can mean you will need to spend thousands on a legal defense.

In the case of shooting dogs questions that you might want to have answers readily on hand for questions that include:

Have you lost livestock previously? Can you provide witnesses and/or documentation?

How do you know it was dogs? Witnesses, tracks, type of damage, documentation?

How do you know the dogs shot were an imminent threat and not just 'playing'? Signs, location, behavior. Witnesses, evidence, documentation?

How do you know these dog/s were not just wandering by? Location, proximity to livestock. Threatening behavior?

Keep these answers in mind. They both allow you to firmly assert your right to defend your livestock and to defend against any charges that may come your way. First impressions and presentation matter. Hopefully this is handled without the law and courts getting involved (SSS) but paying attention to there details, documenting them if possible, may pay off big if they do.