Yes, is there any water at all on the top of your dashboard? Or do you see water weeping through the grab handle on the A-pillar? If so, you very likely have a windshield leak, either across the top or running down the side. Black rubber weather sealant will take care of it, do not use any kind of silicone as it is corrosive.
Other things to check:
1. Remove the inner door seal and look for a pinch weld at the apex near the front top of the window. Very likely there could be a nice hole there that water pours down into easily, as with the above, black rubber weather sealant should be applied, no silicone.
2. While you have the seal off the inner side, look along the top of the bar that the seal sits on to see if there are any gaps between the body of the car and the bar itself. Chrysler seemed to have not used any weather sealant here at all and just relied on a baked-on sealant between the body and the bar, and then paint to keep it water tight. That doesn't work long term, so after these cars are 10+ years old? Seal it up with black rubber weather sealant.
3. Get a ladder and inspect the bolts holding the roof rails on the top of the car. The ones just behind the front plastic cover tend to rust the worst. Change out any rusted ones, be sure to use loc-tite or a similar sealant on the threads and then sealing it over on top isn't a bad idea either (you can use silicone on this area though, no paint here so it's okay).
Okay, this is like a Jeep Commander greatest hits bullet point. The leaking sun roof drain tube. Like a lot of folks, I had this issue for a while and it was really confounding. In my case, it seemed to have been exacerbated by the sun roof frame. The tubes clogged at a point that the XK sat...