My water tank filling up in the back where the water is connected to city water the tank is full and shouldn't be because I'm on city water

no info generic answer check valve - faucet --failure open access and check lines valves pump

if separate fill holes then bad check valve at water pump

The water connection is typically on the driver's side outside wall. You most likely have a valve that switches between "Fill" (a ~60 gal. water tank) and "City pressure" that allows the water pump to be turned off. If the water fill isn't visible on the sidewall, check in the wet bay for the connection.

Check to see if you have a valve labeled for tank fill. It sounds like you have a single connection to use city water or fill your tank and it is in the tank fill position. The water you are seeing would be coming from the tank over flow.

Many RVs have the plumbing to fill the fresh water tank from the city water hook up. This valve is usually near the city water hook up and labeling is similar to "city water" and "tank fill". Another anomaly from leaving the valve in the "tank fill" position is that, when not connected to city water, the on board pump may run continuously and the water volume is very low.

it does exactly what it is supposed to do,shut off water when it is full

Probable cause would be a leaking check valve in the pump.

On the RV the city water and discharge from the fresh water pump are tied together. When on city water the discharge of the pump will have city water pressure on it. If the internal check valve on the pump is leaking, water will flow through the pump backwards and into your fresh water tank.

Yes. Open the outside panel, usually located close to or beside the city water inlet. Should be a diagram showing "normal", "tank fill" and "winterize." Use "fill" to fill the tank. Water will run out the underneath drain when full. I recommend a water pressure limiter just in case the city water pressure is excessive. You can rupture a line or the tank if too high. Rare, but it does happen.

Flip the valves to "normal" to use the city water. If boondocking, the pump will pull from the fresh water tank directly. No need ot change anything.

It is likely one of two things, either your RV has a waterline to your fresh water tank that allows you to fill that tank when you are hooked to City water, or the check valve on your water pump is bad and it is allowing city water to fill your fresh water tank. Make sure your freshwater tank is empty, have someone turn the city water on while you watch the freshwater tank... you should be able to see where it is filling from....if it is filling from the water line that run to the water pump, the check valve is bad, if it is filling from a city water fill line, locate the valve on that line and close it. If it is indeed the water pump check valve...you can either replace the pump, or add a cheap inline check valve, like a sharkbite check valve.. they run like 12 to 15 dollars.. install in seconds....you just cut the pex pipe then shove the ends into each end of the check valve.

Where does it leak from? You city water supply line?