Cars gives out smoke from under the hood mainly from the radiator?

2002 honda civic 2.0l type r, 76,000, the cars gives out smoke from under the hood mainly from the radiator, however i've checked the oil which is fine, there's no gunk on the oil cap, the heaters work and they give out warm but not hot air, i've taken it to a local garage and they checked it there is some water dripping underneath. Loses water but not much. Does the radiator need replacing?Please help.