Hi, I'm Heather, an attorney with 15 years experience and I'd like to assist for informational purposes.
There isn't really any law that states that the manager has to tell you who made the complaint. The management probably has that policy, because if they tell you who it is, there is a potential that there could be hostilities or confrontations come up, and that would cause more problems for everyone.
On the other hand, you are totally right, that they need to tell you what the complaint was about. You cannot correct a problem if you don't know what the problem is. You don't know if it's about noise, or the dog going to the bathroom in the wrong place. You have no idea and cannot fix the problem without that information.
I think you need to write a letter to management stating that you are happy to take care of any issues with your animals, but since they have not identified any specific issue, you don't have anything that you are aware of that needs to be corrected. Until they give you the nature of the problem, then you can't take care of it.
Has that helped answer your question?