As others have said - clean the drip holes in the drain pan located under evaporator. If your going up to remove the shroud you might consider spending additional time and clean the evaporator coils - they tend to be ignored by many/most because they are hidden by a metal shroud (which requires removing a dozen or so screws). A clean evaporator will improve the overall performance of the air conditioner.
Another possibility is that the air conditioner gasket is old or needs to be tightened. Lots of threads on how to do that - but don't over tighten the gasket.
Hope this helps.