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Hard to say without any pictures?
I would clean everything up good and watch where the oil is coming from.
On my STR I had the oil cooler lines weeping where the rubber hose is crimped onto the metal tube. Hard to see because as the oil weeps out the air flow throws it all over the front of the engine. My fix was to cut off the metal crimp and replace the rubber hose reusing the factory steel tubes and adding 2 clamps per connection. Never had a problem after that.
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Like club says clean up the area real good. Then get it up high enough to run the engine and look. I found the oil filter adapter plate leaking on my 06 str. There is also the front crank seal and lower timing cover gasket as a possibility if coming above the oil filter. The 03 and 06 have different oil cooler setups so i am not familiar with the hose routing. If club saiys check yours then he definitely knows for sure. I now have a small nuisance leak at the bottom of the timing cover myself.
The metal line connecting to the oil filter housing above the filter has a o ring seal that I replaced. there is still oil coming for somewhere but this stopped the majority of the leak....