I'm guessing it does leak while it's running, you just don't leave it running in one spot to get a puddle.
The "overflow" tank is actually a reservoir to the system. It has a "low" mark and a "full" mark. Should always be fluid in that tank.
If it's empty it's because the leak occurs when running and lowers the fluid level in the radiator. Then when the engine cools it sucks replacement fluid from the overflow tank until it empties the tank.
You didn't mention whether you've had to add fluid at any time?? Also didn't mention whether the engine is getting hot or not??
And lastly, normally you don't add fluid to the radiator. It's added to the overflow tank to maintain a proper level. In your case I'd probably open the radiator and top it off, then fill the overflow tank to the appropriate level. Then continue the search for the leak.