First, one should consider the ceiling stain is a result of water and there are many reasons why stains may occur on the ceiling. Often, water sources such as condensation development from air conditioning ducts and service lines in humid climates, drain overflow pans in the attic, roof openings for the plumbing vents (pipes), etc.…… should be considered as opportunities for water intrusion. One should look in the attic or living area of your house above the ceiling stain to inspect any of these practical reasons. Keep in mind, water can travel great distances along wires, roof framing, etc. before gravity takes over and the water drops onto the ceiling. Look for clues of long-term water activity like discolored wood framing, water stains, or matted and discolored insulation. Of course, if there is a bathroom or utility room over the ceiling stain, logic suggests a thorough inspection of the plumbing lines and drains in these rooms as your first step.
If there are changes in the roof configuration above or near the ceiling stain, careful evaluation of the roof flashing may lead you to the cause of the water. Often, roof flashing will not be seated or installed properly at dormers, walls, and trim features allowing rainwater or snow melt to travel beneath and around the flashing. Do not overlook gaps in wall trim and siding as causes for water entry.
In more complicated searches for water intrusion, entry sources, such as plumbing vents over a second story living area, combined with the second story living area, can create complex searches for water pathways. Create a sketch of your house and make note of your findings.
If you are a do-it-yourselfer, do not overlook the smallest of details and you can figure this out. Be careful and good luck on your search.