Can animal controll issue citations on Private Lands?

I live in a private association with 130 5 acre or more lots. The association is in 6 sections. I have 5.063 acres the road that leads to my property is a private association road. my property does not touch anywhere on the county! My neighbor is a drunk, and likes to cause trouble she turned me in saying that my dog keep chasing her car when she goes up the road, and that it might cause an accident. She is a drunk, and DUI's cause more accidents than anything!!! anyways my dog guards the property. my concern is can animal controll issue citations on private property, or private roads? The roads within the association I live are for landowners only! no public access without permission. We pay dues for the roads, our roads are maintained by the association, not the county. We have posted signs that say no tresspassing without permission. (Landowners,board members etc:) Law enforcement cant issue citations why is animal control? Also animal controll never saw my dog at large, my neighbor called and complained! animal controll called me by telephone and the dog she described was not even my dog. a week later she mailed me a citation, but still she never saw my dog chasing cars! What do i expect, what can i do? Im on private property, on private roads. There are on average 2 cars a day driving on this road near my property so how is a dog going to cause an accident?