A number of publicly owned lands can be considered off limits, especially for hunting. In fact, most city land is off limits to hunting. Additionally, land can be off limits for safety or other reasons such as water retention basins, etc. Don't assume all land is public and you can do whatever you want just because the city owns it.
Anyway, use the commonweath maps public hunting land overlay to see if public hunting is allowed.
Here is the map for the forest: http://kygeonet.ky.gov/kdfwr/index.html ... WR_ID=9089
Also, if you post the area you're talking about, I can probably give you an answer. I've hunted up near there before and I'm familiar with the land. What city are you talking about? If it is forest land, it probably is open to hunting.