Firstly you should find the source of the damp seeking the help of a professional (independent surveyor). He or she may establish the cause and the type and cost of treatment that may be required to combat the damp. As was held by the Madrid Court of Appeal in its ruling of 14 Nov 2008 if you are thinking of taking someone to court you must get firstly an accurate diagnosis of the problem (in writing).
If the problem is caused by damp in common parts such as pipes, pillars, girders, forged supporting walls section 10 (1) of the Horizontal Property Act 49/1960 is applied
´The community is obliged to carry out works necessary for the proper upkeep and maintenance of the building and its facilities to ensure appropriate structural conditions, imperviousness, habitation and safety`.
It is clear that the Act provides for the performance by the community of a particular duty of maintenance therefore every owner injured by failure to perform that obligation is entitled to compensation.
Thus, where the source of the damp is not located within a unit, the community must carry out the necessary repair works and could be liable under negligence. This is a very usual case dealt in Spanish courts namely, rulings of the Court of Appeal in Madrid 14-01-2009, 11-06-2007 or CA in Alicante 25-09-2006 among others.
Whether the community is liable or not in the case of damp caused by building defects on common parts is not clear. In favour the ruling of CA Madrid 16-04-2008, against the CA ruling in Madrid 20-6-2005
If there is no common part involved it shall be a case between you and the owner of the above apartment (in this case the commonhold is discharged because there are no common parts involved.), then section 9 (1) (a) shall be applied
9 (1) The duties of each owner include:
(a) to respect the general installations of the commonhold and any other common parts: whether for general or exclusively use by all or any of the co-owners; whether included in their flats or premises or not.
Ruling of CA in Madrid, 27 June 2006 dealt with a similar case of yours ruling in favour of the lower apartment
If I were the lawyer of your neighbour I will hold that the damp is caused by a building defect thus my client is not accountable. I will try to move the liability to the architect or to the building firm