Plumbing – Ceiling leaking from upstairs bathroom ONLY when water supply is turned OFF

All the advice so far about ice damns is valid. However, if there are no dams or visible water on the roof, then you will need to crawl up in the attic and start looking for the wet areas that are wicking into your ceiling. The insulation may have been soaked before you got a chance to clear the roof. Obviously if wet insulation is found, it must be removed. Another problem I have come across in a few situations like yours, no dam, but slow moisture stains keep developing, came from improperly installed "proper vent" from the soffit vents to the air space in the attic. In a few cases, the open upper end of the proper vent was blocked or covered with insulation and condensation formed on the top side of the drywall right along the wall. In a couple of cases, no venting was used from the soffit and insulation was packed into this area instead. In either case, you will have to get up there and move the insulation in the affected areas and look for the moisture. Also look for any tell-tale water stains on the rafters or trusses that may have been a leak from above.

What this could be is that you have a slow leak from the floor above. Probably a water feed rather than a drain. Although it could be from the heating system if you have a water or steam system with radiators. When you turned the water on the house it started to drip, and the ceiling soaked it all up. Eventually the ceiling became saturated and started to drip onto the floor.

If you do have a slow leak then obviously you need to find the source. It's probably a leaky pipe joint, or maybe a loose compression fitting. The only way you're going to find it is to get access, as for how that completely depends on your house's construction. There may be a panel in front of the bath that can be removed, etc.

What you need to do is meticulously go through the whole bathroom above and look for any kind of access to pipes you see, and look for signs of dripping moisture, oxidation on the pipes, or hard water deposits. As it sounds like the whole ceiling needs to come down on the floor below do that first, then use that access to find your leak.

As for how to fix it if it's a compression fitting get out your wrench and have at it. If it's a solder joint or a bad pipe get a plumber in unless you have the tools and the experience. Good luck!