One thing for sure.....city water leak is NOT coming from grey/black tank/drains.
Unless you have a black tank flush connection and have hooked up you water supply to it and the tank is full/overflowing......which is a whole different problem.
Water leaking from rear of rig when connected to city water is either a 'low point' drain valve still open OR you have a cracked line/fitting in plumbing system.
What is at back of rig??
Kitchen, bathroom, outside shower, city water connection???
Crawl under rig and investigate.
Open EVERY door, cabinet, access panel inside & outside.
FIND the source of leak.........water will cause LOTS of damage.