Rather than trace the route of the dripping overflow you might consider looking into the places where the pipe might run to.
These may be:
Cold Water storage tank in the loft
Smaller, Central Heating header-tank in the loft
Any toilet cisterns
Lift the lids and look inside - you should easily see which is the culprit.
If you eventually intend to call in a tradesperson to solve the problem then don't bother yourself with all the inspection and clambering about - let the hired-hand do it instead.
Good luck...
Peccavi, September 2009