For manual landings there are no crosswind limits given in the AFM for the A320 (like for most aircraft). It's up to the operator to define limits (if they want). Often the demonstrated crosswinds are used as limits. It is my experience that many operators do struggle with this topic.
More info on this topic can be found in:
Crosswind Certification - How does it affect you?
http://www.nlr.nl/id~5114/lang~en.pdf