There is often a check valve in the pump to allow pressure built up not to leak back into the tank. There also may be a check valve between the city water hook up and water system to prevent back flow into the campground system if pressure dropped. One or the other of those check valves is leaking. The pump check valve maybe replaceable, you didn't mention the make and model. The check valve in the city water line also might be easy to replace, it would either be inline or a part of the city water hook up.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI