Open alleyway through my yard?

So I bought a house in town about a year ago. I'm hoping someone can tell me about what to do about an alley way that runs by my house. Well you really would not know it was one do to there are no markings or anything and it is pretty much what I thought to be my driveway. I've went to my city hall and they said in fact it is an open alley way. Obviously they haven't looked at it in a long time. It does not connect to anything and has a fence cutting it off about midways were the alley supposedly is. From my understanding the alley way is suppose to connect my street to another one but it doesn't. Anyone else ever had to deal with something like this?