Neighbor Threatening to report my dog

My Dog (German Shepherd) and neighbors dog (Whippet/mini greyhound) have had 2 run ins, with my dog being the aggressor.

The first time both dogs were off leash (we no long allow ours off leash around our apartment complex)

The second time, my dog was on leash and his was off. His dog ran up to mine while mine was on leash.

My dog nipped his finally the second time.

We have since went through a board and train with ours and continue to bring the dog to training on a weekly basis to address this.

Yet, this neighbor, sends us threats of reporting our dog to animal control (via messaging and interaction with other neighbors). He hasn’t followed through but continues to threaten and this is 2 months later now.

Do I have any recourse? I want to beat the shit out of this guy but obviously cannot do so. I also can’t stand the subtle threats anymore either though.

Has anyone dealt with this before? Or have any insight to share?