If you are leaking water when connected to a water source, you need to trace the leak. It's either a connection in your hose and filter, or you have the valves for city/fresh water in the wrong position and are overflowing your tank. If your valve is in the correct position it is possible you have a bad valve. This is odd though because if your tank was full and overflowing your pump would not continuously run - unless you have a leak.
Given the limited information, I am going to guess you have a leak somewhere in the supply line. This guess is based on the fact that your water pump continues to run. It wouldn't do that if your water tank was full and overflowing.
What does the reading say on your fresh water tank?
Are your winterization valves in the proper position for use?