I think you should ask the HOA for a hearing so that you can correct the record that your neighbor has laid.
I am an Attorney-at-Law, licensed to practice law only in the state of California. Unless we have both signed a formal retainer agreement, you are not my client, and my discussion of issues does not constitute legal advice. Opinions expressed herein are those of the author, and do not necessarily represent the opinions of those who hold other opinions.
Surveillance cameras are increasingly affordable. You could even put a game camera in the yard to monitor your dog and find out if he is being harassed or let loose.
The foregoing is for general information purposes and does not establish an attorney-client relationship.
Yes, you should be worried. One, the HOA can legally do this. Two, once Animal Control (which is the County) opens a file on an animal, with each complaint, the animal becomes more vulnerable to confiscation. Cities usually have very harsh remedies too. What is the underlying problem? You do not say. Usually, it is barking. Take care of the underlying problem.
We do not have an attorney-client relationship. I am not your lawyer. The statements I have made do not constitute legal advice. Any statements I have made are based upon the very limited facts you have presented, and under the premise that you will consult with a local attorney. This is not an attempt to solicit business. This disclaimer is in addition to any disclaimers that this website has made. I am only licensed in California.
First, it depends on how your community's CCRs address dogs. The may be a provision which allows the HOA to demand that you get rid a dog that creates a nuisance or creates a danger to the community. If he CCRs allow for such action, the HOA can demand that the pet be removed. I have seen this happen.
Second, before the HOA requires you to remove the dog from the community, it must conduct a due process hearing in which you will be given the opportunity to explain your position and ask that the HOA allows you to keep the dog.
In the meantime, if you believe that the neighbor is attempting to let your dog out, you might consider locking your gate and/or keeping the dog inside when you are not home to supervise.
You might want to contact an attorney to assist you in this matter