Water leaking from overflow valve on city water

From your description, I believe the valve you are talking about are the low point drains for the water system. In normal operation, they will be closed. Depending on the maker, they could be push-pull or quarter turn valves located somewhere above the point where you see the leak.
Try using the valve a couple of times quickly to clear the valve and see if your leak stops as debris may be preventing them from fully closing. Worst case may be to replace them.