Sounds to me like a heater box leak. there is one way to tell if it is. soak up some of the water, and if it is green, it is a leak in yoru heater box. if it is clear it coudl be running in thourgh the vents on the outside of the car locate dunder the windshield.
If it is clear water, and happens only with the air conditioner on, then it is the evaporator runoff from the AC system. Somehow the hose was severed and now the water leaks into the vehicle instead of out to the road.
There is a technical service bulletin (TSB)related to this problem. If you can find a nice Honda dealer, they can print you out a copy of this TSB outlining the repair.
I have a 96 Civic and found water leaking in on the driver's side such that the carpet was wet. Sealed around the rubber grommet where the wiring harness went through the firewall under the hood.
For your problem, you will likely have to remove the fender and apply new sealant. Again, get the TSB. This TSB might even be shown (actual diagram), if I recall, in the book 'Lemonaide' (spelling?)for cars.
This is an update to my info giving reference to a TSB for this problem. The TSB no. is X-1-95 (originally found from Alldata as TSB 92-050. So try both. The bulletin is titled 'Water Leak From Seam Under Corner of Dash'. It applies to model years 92-97.
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