We are full time RVers connected to commercial water source for fresh water. Yesterday, I noticed the freshwater tank overflow dripping water and that the tank is full. Seems the commercial water source is back-flowing into the freshwater tank. Do I need to replace the water pump?

That depends on the pump. You can try cleaning the check valve on the pump first. On some pumps, the check valve is replaceable. For now, assuming your freshwater tank is clean, you can shut off the city water, then use your water pump from the freshwater tank until it's empty. This may clean the check valve for you.

Shurflow pump...running on the pump for a few hours resolved the problem. Thank you.

Glad things worked out.