I have a 2003 Honda Civic its leaking oil from the engine while its at rest (not running). Very concerned?

It is not a lot of oil, not enough to spill to the ground, but it is on the engine and I fear it may get worse. The Mechanic thinks its from the head and might be a gasket, but I have my doubts. I cleaned the area myself and started the car. No oil leak. When I switched off then I saw the oil started leaking. I believe it could be a seal but I'm no mechanic. My question is, how serious is an oil leak that does not spill over to the ground, and what can be the possible reason for it only happening when the car is off and not while its running?
Thanks in advance for any sound advice and answers:-)

Well, you say that the mechanic said "it might be the head" and you say that you cleaned the area yourself (which alludes to easy access). This leads me to believe that you are probably facing a leaky valve-cover gasket (on top of the head). But I can't see it from here, maybe you could post a pic of the area?

First look or get someone to jack the car up then LOOK at the bottom of the engine, look for oil and damage. Depending on what you see continue from there, wipe away all the oil, then keep looking until you find the source of your leak.