Chris,
Typically the tanks referred to as holding tanks store the gray and black water for disposal. If those are fill from city water, you tap leaks that you need to repair.
If you are referring to where the potable water is stored, that is regularly called a water tank or potable tank. If that is filling from the city water connection then either the fill valve (not all RVs have) that is there to make this convenient is leaking or the system check valves are leaking.
Both of the above are why those of us that have been at this a while don't leave the city water pressurized when it is not being watched (you are not there or are asleep). It doesn't take much to go wrong to have wet floors.
Matt