What do you do with a neighbor who complains a lot?

[Jessie]

I live in an apartment complex I am on the lower level and the man, lets call him X, who lives above me complains a lot about the noise level around the complex. Granted this complex is over all a very quit complex even when the children are playing outside and the dogs barking but that doesn't bother me one bit. The thing that bothers me is X who every time there is a bothersome noise he comes down and complains to me like it was my family making the noise. When I leave my dog barks and today when I was leaving to take my son to his daycare X was leaving and he stops right in front of the window where my dog was and tells her to stop barking. I told X that he has no right to tell my dog to stop barking and if you talk to her she is just going to bark at you some more. I also told him because I am tired of his complaining that if he doesn't like the noise level around this complex, he should move.
My question is do I have a right to complain to managment about him?
Excuse me feeling mutual but I do take responsibility for my dog barking. I do not deny that she barks But when I am away how can i tell her to stop barking when i am not there and no i will not get a shock collar. My dog however is not the only dog in the complex that barks he just assumes that it is my dog. So before you start being an ass why dont you get your facts straight.
Plus my dog doesn't bark all day and all night just when I am leaving but she will go lay down after 10 minutes. How do I know this because I have tested it. There are some times when I am home that when we are playing she will bark out of excitment. But its not like she is chained up in a backyard barking 24/7 because she isn't.

 

[tulip_five]

You can go to management, but they will probably side with X. If the dog becomes too much of a problem they will probably ask you to get rid of him. It will really all depend on what the lease says.